ELEMENTS 



OF 



SURVEYING 



AND 



LEVELLING; 



DESCRIPTIONS OF THE IISrSTRUiyiENTS AND THE 
NECESSARY TABLES. 



By CHAKLES D.AYIES, LL.D., 

AUTHOR OP A rULL COUBSB Oj" MATHEMATICS. 



< 



A. S. BAEITES & COMPANY, 

NEW YORK AND CHICAGO. 

1870. 



DAVIES' 

COUESE OF MATHEMATICS. 



Davies' Primary Arithmetic and Table-Book — Designed for Beginners; 

containing tlie elementary tables of Addition, Subtraction, Multiplication, 

Division, and Denominate Numbers; with a large number of easy and 

practical questions, both mental and written. 
Davies' First Lessons in Arithmetic — Combining the Oral Method with 

the Method of Teaching the Combinations of Figures by Sight. 
Davies' Intellectual Arithmetic — An Analysis of the Science of Numbers, 

with especial reference to Mental Training and Development. 
Davies' New School Arithmetic — Analytical and Practical. 
Key to Davies' New School Arithmetic. 
Davies' Grammar of Arithmetic — An Analysis of the Language of Numbers 

and the Science of Figures. 
Davies' University Arithmetic — Embracing the Science of Numbers, 

and their Applications according to the most Improved Methods of 

Analysis and Cancellation. 
Key to Davies' University Arithmetic. 

Davies' Elementary Algebra — Embracing the First Principles of the 
Science. 

Key to Davies' Elementary Algebra. 

Davies' Elementary Geometry and Trigonometry — With Applications in 
Mensuration. 

Davies' Practical Mathematics — With Drawing and Mensuration applied 
to the Mechanic Arts. 

Davies' University Algebra — Embracing a Logical Development of the 
Science, with graded examples^ 

Davies' Bourdon's Algebra — Including Sturm's and Homer's Theorems, 
and practical examples. 

Davies' Legendre's Geometry and Trigonometry — Revised and adapted 
to the course of Mathematical Instruction in the United States. 

Davies' Elements of Surveying and Levelling — Containing descriptions 
of the Instruments and necessaiy Tables. 

Davies' Analytical Geometry — Embracing the Equations of the Point, the 
Straight Line, the Conic Sections, and Smfaces of the first and second 
order. 

Davies' Differential and Integral Calculus. 

Davies' Descriptive Geometry— With its application to Spherical Trigo- 
nometry, Spherical Projections, and Warped Surfaces. 

Davies' Shades, Shadows, and Perspective, 

Davies' Logic and Utility of Mathematics— With the best methods of In- 
struction Explained and Illustrated. 

Davies' and Peck's Mathematical Dictionary and Cyclopedia of Mathe- 
matical Science— Comprising Definitions of all the terms employed in 
Mathematics— an Analysis of each Branch, and of the whole, as forming 
a single Science. 



Entered according to Act of Congress, in the year one thousand eight hundred and seventy, by 
Charles Davies, in the Clerk's Office of the District Court of the United States for the houthera 



Charles 

District of New York 



V LlTTLK, Kennie & Co., Stereotvpers, 615 and 617 Broadway, New York. 



3 



PREFACE 



7 

The Elements of Surveying, first published in 1830, was 
designed as a text-book for the pupils of the Military 
Academy, and in its preparation little regard was had to 
the supposed wants of other institutions. 

The work, however, was received by the public with more 
favor than was anticipated, and soon became a leading text- 
book in the Colleges, the Academies, and the higher grade 
of Schools. 

For the purpose of adapting it more fully to the supposed 
wants of these institutions, many changes have been made 
since its first publication ; and the present edition will be 
found to differ, in many respects, from those which have pre- 
ceded. 

It has been the intention to begin with the very elements 
of the subject, and to combine those elements in the sim- 
plest manner, so as to render the higher branches of Plane 
Surveying comparatively easy. All the instruments needed 
for plotting have been carefully described; and the uses of 
those required for the measurement of angles are fully ex- 
plained. 

The conventional signs adopted by the Topographical 
Bureau, which are now used by the United States Engi- 
neers in all their Charts and Maps, are given in plates 
5 and 6. 

Should these signs be generally adopted in the country, 
it would give entire uniformity to all maps and dehneations 



4 PREFACE. 

of ground, and would establisli a common language by 
which all the peculiarities of soil and surface could be 
accurately represented. 

A full account is also given of the system adopted in the 
survey of the public lands; and, although the method is 
simple, it has, nevertheless, been productive of great results, 
by defining, with mathematical precision, the boundaries of 
lands in the new States, and thus settling their titles on an 
indisputable basis. 

This method was originated by CoL Jared Mansfield, 
whose great acquirements in science introduced him to the 
notice of President Jefferson, by whom he was appointed 
Surveyor-general of the Northwestern Territory, in the early 
part of the present century. 

Among the changes which have been made in the present 
edition, and which must be very acceptable to Practical 
Surveyors, are the methods of laying down Railroad Curves, 
Section Levelling for Excavation and Embankment, and 
the article on Mining Engineering. For the first of these, 
I am mainly indebted to Professor Plympton, of the 
Brooklyn Polytechnic Institute, who has happily combined 
science and art, both in his methods of teaching and in his 
practical operations in the field ; and for the latter, to Pro- 
fessor Peck, of Columbia College, to whom education and 
science are indebted for much valuable labor. 

FiSHKiLL- ON- Hudson, June, 1870. 



CONTENTS. 



BOOK I. 

LOGARITmiS AND TRIGONOMETRY. 
SECTION I. 

LOGAEITHMS. rAOK 

Of Logarithms 9 

€reneral Piinciples 11 

Table of Logarithms 12 

Use of Table 13 

Multiplication by Logaritlims 17 

Division by Logarithms 18 

Arithmetical Complement 19 

Raising of Powers and Extraction of Roots 23 

SECTION II. 

Geometki€Al Cokstkuctioks. 

Diyiders 23 

Ruler and Triangle 23 

Scale of Equal Parts 25 

Diagonal Scale of Equal Parts 26 

Scale of Chords 1 27 

Semicii-cular Protractor 28 

Sectoral Scale of Equal Parts 29 

Guntefs Scale 81 

Solution of Problems 31 



b CONTENTS. 

SECTION III. 

PlAKE TrIGOI^OMETRY. paqb 

Plane Trigonometiy 37 

Division of the Circumference 37 

Definitions of tlie Trigonometrical Lines 38 

Table of Natural Sines 39 

Table of Logarithmic Sines 40 

Theorems 44-47 

Solution of Triangles 47-56 

Solution of Right- Angled Triangles 56-57 



BOOK 11. 

PLANE SURVEYING. 

SECTION L 

Measurement of Lines and Angles. 

Definitions 58-60 

Measurement of Lines and Angles 60 

Measurement of Distances 60 

Measurement of a Horizontal Line 61-64 

Standard of Measure 65 

Measurement of Angles 65 

Of the Theodolite 66-73 

Verniers 73-75 

]\Ieasurement of a Horizontal Angle with the Theodolite 75 

Measurement of a Vertical Angle 76 

Measurements with the Tape or Chain 78-84 

Applications to Heights and Distances 84-94 

SECTION IL 

Area or Contents of Ground. 

Area or Contents of Ground 94-97 

Problems relating to Area or Contents of Ground 97-108 



CONTENTS. . 7 

SECTION III. 
Compass Sueyeyi2hG. page 

Definitions lOS-110 

Surveyor's Compass 110 

Work on the Field 112-117 

General Example 117 

Traverse Table 121 

Balancing Work 125-129 

Double Meridian Distances and Area 129-140 

Problems 140-145 

Laying Out and Dividing Land * 145-153 

Public Lands 153-157 

Variation of the Xeedle 157-162 

To find the U'ue Meridian 163 

SECTION lY. 
Teiak"gulatio:s". 

Definitions and General Remarks 167-170 

Uses of the Theodolite 170-173 

Filling up the Survey 173 

Use of Compass 173-175 

Plane Table and Uses *^ 175-181 

Plottmg Work 181 

Circular Protractor 181 

Various Methods of Plotting 182-186 

Maritime Surveying 18&-189 

BOOK III. 

LEVELLING AND ITS APPLICATIONS. 
SECTION I. 

Levelldsg. 

Definitions and Principles 190-193 

Description of the Y Level 192-196 

Levelling Rods 196 

'■^vellmg in the Field. 199-206 



S CONTENTS. 

SECTION IL 
Topographical SuRVEYiifG. pao» 

Definitions and Principles 206 

Examples and Plotting 207-219 

SECTION III. 

Railway Curyes. 

Definitions and Principles 219-222 

Location of the Curve 222-224 

Location by tlie Chain alone 224-227 

Location by two Transits 227 

Laying off the Ordinates 229 

SECTION IV. 

Section Levellii^^g. 

Definitions and Principles 230-236 

Drawing the Profile 236 

Establishment of the Grade 237-243 

Cross-Section Levelling 244 

Setting Slope Stakes 245-254 

Computation of Earthwork 255-258 

SECTION V. 

MlN"IN^G Eiq"QIJ?'EERIi^G. 

Definitions and General Notions 259 

Traversing— Compass— Miner's Scmich-cle 260 

Field Book 262 

Method of Traversing with the Theodolite 263 

Field Book 264 

Modes of Connecting with Surface Survey 265 

Reducing the Traverse— Office Book 267 

Method of Plotting the Traverse oh the Surface 268 

Method of Plotting the Traverse on Paper 269 



ELEMENTS OF SURYEYING. 



BOOK I. 

LOGARITHMS AND TRIGONOMETEY. 



SECTION I. 
LOaARITHMS. 



1. The Logakithm of a number is the exponent of the 
power to which, it is necessary to raise a fixed number, to 
produce the given number. 

The fixed number is called the hase of tM system. Any 
positive number, except 1, may be taken as the base of a 
system. In the common system, the base is 10. 

2. If we denote any positive number by n, and the 
corresponding exponent of 10 by p, we shall have the 
exponential equation, 

lOP = w (1.) 

In this equation, p is, by definition, the logarithm of n, 
which may be expressed . thus, 

p = log n (2.) . 

3. From the definition of a logarithm, it follows that, the 
logarithm of any power of 10 is equal to the exponent of 
that power : hence, the formula, 

log {lOy =z log n = p. • . • . . (3.) 



10 ELEMENTS OF SURVEYING. [BOOK I. 

If a number is an exact power of 10, its logaritlim is a 
whole mtmler. 

If a number is not an exact power of 10, its logaritlim will 
not be a whole number, but will be made up of an entire part 
plus a fractional part, which is generally expressed decimally. 
The entire part of a logarithm is called the cJiaracf eristic j the 
decimal part is called the tnantissa. 

4. If, in Equation (3), we make p successively equal to 
0, 1, 2, 3, &c. ; and then equal to — 1, — 2, — 3, &c., we may 
form the following 

Table. 



log 1 = 








log 10 = 1 


log .1 


= 


-1 


log 100 = 2 


log .01 


z=z 


-2 


log 1000 = 3 


log .001 


= 


-3 


&c., &c. 


&c., 


&C. 





When a number lies between 1 and 10, its logarithm lies 
'between and 1; that is, it is equal to 0, plies a decimal; if a 
number lies between 10 and 100, its logarithm is equal to 1, 
plus a decimal ; if between 100 and 1000, its logarithm is equal 
to 2, plus a decimal ; and so on : hence, we have the following 

EuLE. — The characteristic of the logarithm of any whole num- 
ber is positive, and numerically 1 less than the number of places 
■of figures in the given number. 

When a decimal fraction lies betweern .1 and 1, its logarithm 
lies between — 1 and 0, that is, it is equal to — 1, plus a deci- 
mal; if a number lies between .01 and .1, its logarithm is 
equal to — 2, phis -.a decimal ; if between .001 and .01, its 
'logarithm is equal to — 3, plus a decimal; and so on: hence, 
the following 



SEC. I.] LOGAEirmiS. 11 

KuLE. — The characteristic of the logarithm of a decimal 
fraction is negative, and numerically 1 greater than the 
numher of (fs that immediately follow the decimal point. 

The characteristic alone is negative, the mantissa heing 
always positive. This fact is indicated by writing the nega- 
tive sign over the characteristic: thus, 2.3T1465, is equivalent 
to — 2 4- .371465. 

!N"OTE. — It is to be observed, that the characteristic of a 
mixed number is the same as that of its entu-e part. Thus, the 
mixed number T4.103 lies between 10 and 100 ; hence, its loga- 
rithm lies between 1 and 2, as does the logarithm of 74. 

GeXERAL PeDsCIPLES. 

5. Let m and 7i denote any two numbers, and p and q 
their logarithms. We shall have, from the definition of a loga- 
rithm, the following equations, 

10^ = m (4.) 

lO*? = n (5.) 

Multiplying (4) and (5), member by member, we have, 

lOP+2 = mn; 

whence, by the definition, 

j5 + ^ = log {/U/l) (6.) 

That is, the logarithm of the product of two nximlers is equal 
to the sum of the logarithms of the numbers. 



6. Dividing (4) by (5), member by member, we have, 
whence, by the definition. 



n 



p - q 



= ^°^(f) (^•) 



12 ELEMENTS OF SURVEYING. [BOOK 1. 

That is, the logarithm of a quotient is equal to the logarithm of 
the dividend diminished hy that of the divisor, 

7. Raising both members of (4), to a power denoted by t, 

we huye, 

10^' = m'; 

'whence, by the definition, 

pt = log m* (8.) 

That is, the logarithm of any poiuer of a numler, is equal to 
the logarithm of the number, multiplied iy the exponent of the 
potver. 

8. Extracting the root, indicated by r, of both members of 
(4), we have, 

IC = y m; 
whence, by the definition, 

f = log ^. ..... . (9.) 

That is, the logarithm of any root of a number, is equal to the 
logarithm of the number divided by the index of the root. 

The preceding principles enable us to abbreviate the opera- 
tions of multiplication and division of numbers, by the addition 
and subtraction of their logarithms. 

Table of Logaeithms. 

9. A Table of Logarithms, is a table by means of which 
we can find the logarithm corresponding to any number, or the 
number corresponding to any logarithm. 

In the table appended, the complete logarithm is given for 
all numbers from 1 up to 100. For other numbers, between 
100 and 10,000, the mantissas alone are given ; the characteristic 
may be found by one of the rules of (Art, 4). 



SEC. l] logaeithms. 1$ 

Before explaining the uses of tlie table, it is to be shown 
that the mantissa of the logarithm of any number is not 
changed by multiplying or dividing the number by any exact 
power of 10. 

Let n denote any number whatever, and 10^ any power of 
10, j9 being any whole number, either positive or negative. 
Then, in accordance with the principles of (Arts. 5 and 3), we 
shall have, 

log ( ^i X 10^) = log n + log 10^ = i? + log n\ 

but y is, by hypothesis, a whole number; hence, the decimal 
part of the log ( ?j X 10^ ), is the same as that of log n \ which 
tvas to be proved. 

Hence, in finding the mantissa of the logarithm of a num- 
ber, we may regard the number as a decimal, and move the 
decimal point to the right or left, at pleasure. Thus, the 
mantissa of the logarithm of 456357, is the same as that of 
the number 4563.57; and the mantissa of the logarithm of 
2.00357, is the same as that of 2003.57. 





EXAMPLES. 




log 327 


is 


2.514548 


log 32.7 


te 


1.514548 


log 3.27 


ie 


0.514548 


log .327 


te 


T.514548 


log .0327 


(( 


2.514548 



Using the Table. 

1*. To find, from the table, the logarithm of a number less than 100. 

10. Look on the first page, in the column headed "N," 

for the given number; the number opposite is the logarithm 

required. Thus, 

log 67 = 1.826075. 



14 ELEMENTS OF SURVEYING. [BOOK I. 

2°. To find the logarithm of a number between 100 and 10,000. 

11. Find the characteristic by the first rule of (Art. 4). 

To find the mantissa, look in the column headed "N," for 
the first three figures of the number; then pass along a hori- 
zontal line until you come to the column headed with the 
fourth figure of the number; at this place will be found four 
figures of the mantissa, to which, two other figures, taken 
from the column headed " 0," are to be prefixed. If the figures 
found stand opposite a row of six figures, in the column headed 
"0," the first two of this row are the ones to be prefixed; if 
not, ascend the column till a row of six figures is found; the 
first two, of this row, are the ones to be prefixed. 

If, however, in passing back from the four figures, first 
found, any dots are passed, the two figures to be prefixed must 
be taken from the line immediately below. When the figures 
first found, faU at a place where dots occur, the dots must be 
replaced by O's, and the figures to be prefixed must be taken 
from the line heloiu. Thus, 

Log 8979 = 3.953228 > 
Log 3098 = 3.491081 
Log 2188 = 3.340047 

3°. To find the logarithm of a number greater than 10,000. 

12. Find the characteristic by the first rule of (Art. 4). 

To find the mantissa, place a decimal point after the fourth 
figure (Art. 9), thus converting the number into a mixed num- 
ber. Find the mantissa of the entire part, by the method last 
given. Then take from the column headed "D," the corre- 
sponding talular difference, and multiply this by the decimal 
part and add the product to the mantissa just found. The 
result will be the required mantissa. 



SEC. I.] LOGAEITHMS. 15 

It is to be obseryed that when the decimal part of the 
product just spoken of is equal to or exceeds .5, Tre add 1 to 
the entire part; otherwise the decimal part is rejected. 

EXAMPLE. 

To find the logarithm of 672887. 

The characteristic is 5. Placing a decimal point after the 
fourth figure, the number becomes 6728.87. The mantissa of 
the logarithm of 6728 is 827886, and the corresponding num- 
ber in the column "D," is 65. Multiplying 65 by .87, we have 
56.55; or, since the decimal part exceeds .5, 57. "VTe add 57 
to the mantissa already found, giving 827943, and we finally 

haye, 

log 672887 = 5.827943. 

The numbers in the column " D" are the differences between 
the logarithms of two consecutiye whole numbers, and are 
found by subtracting the number under the heading "4" from 
that under the heading "5." 

In the example last giyen, the mantissa of the logarithm of 
6728 is 827886, and that of 6729 is 827951, and their differ- 
ence is 65 ; 87 hundredths of this difference is 57 : hence, the 
mantissa of the logarithm of 6728.87^ is found by adding 57 to 
827886. The principle employed is, that the differences of 
numbers are proportional to the differences of their logarithms, 
when these differences are small. 



4°. To find the logarithm of a decimaL 
13. Find the characteristic by the second rule of (Art. 4). 

To find the mantissa, drop the decimal point, and thus 
consider the decimal a whole number. Find the mantissa of 



16 ELEMENTS OF SURVEYING. [BOOK I. 

the logarithm of this number, and it will be the mantissa 
required. Thus, 

log .0327 = 2.51454:8 

log 378.024 = 2.577520 



5°. To find the number corresponding to a given logarithm. 

14. The rule is the reverse of those just given. Look in the 
table for the mantissa of the given logarithm. If it cannot be 
found, take out the next less mantissa, and also the corre- 
sponding number, which set aside. Find the difference between 
the mantissa taken out and that of the given logarithm; an- 
nex as many O's as may be necessary, and divide this result by 
the corresponding number in the column "D." Annex the 
quotient to the number set aside, and then point off, from the 
left hand, a number of places of figures equal to the character- 
istic plus 1: the result will be the number required. 

If the characteristic is negative, the result will be a pure 
decimal, and the number of O's which immediately follow the 
decimal point, will be one less than the number of units in the 
characteristic. 

EXAMPLES. 

1. Let it be required to find the number corresponding to 
the logarithm 5.233568. 

The next less mantissa in the table is 233504; the corre- 
sponding number is 1712, and the tabular difference is 253. 

OPEEATION. 

Given mantissa, 233568 

Next less mantissa, . . . 233504 . . 1712 

253 ) 6400000 ( 25296. 
.-. The required number is 171225.296. 



SEC. i.] LOGARITHMS. 17 

The number corresponding to the logarithm 2.2335G8 is 
.0171225. 

2. What is the number corresponding to the logarithm 

2.785407? Ans. .06101084. 

3. "What is the number corresponding to the logarithm 
L846741 ? Ans. .702653. 

Multiplication by Logarithms 

15. From the principle proved in (Art. 5), we deduce the 
following 

KuLE. — Find the logarithms of the factors, and tahe their sum; 
then find the numler corresponding to the resulting logarithm,, 
and, it loill he the product required. 

EXAMPLES. 

1. Multiply 23.14 by 5.062. 

OPERATIOlf. 

log 23.14 . . . 1.364363 

log 5.062 . . . 0.704322 



2.068685 .-. 117.1347, product 



2. Find the continued product of 3.902, 597.16, and' 
0.0314728. 

OPEEATION". 

log 3.902 . . . 0.591287 

log 597.16 . . . 2.776091 
log 0.0314728 . . . 2.497936 

1.865314 .-. 73.3354, product. 



Here, the 2 cancels the + 2, and the 1 carried from the 
decimal part is set down. 



18 



ELEMENTS OF SURVEYING. 



[liOOK I. 



3. Find llic contimicd product of 3.580, 2.104(5, 0.8372, 
and 0.0294. Ans. 0.1857615. 

Dn^isioN BY LoGARirnMs. 

16. From the principle proved in (Art. 6), we have the 
following 

Rule. — Find the logari/hms of the dividend and divisor, and 
subtract the latter from the former; then find the nnmher 
corresponding to the resulting logarithm, and it will he the 
quotient required, 

EXAMPLES. 

1. Divide 24163 .by 4567. 

OTERATIO Jf. 

loff 24163 . . . 4.383151 



loff 4567 . . . 3.659631 



0.723520 



5.29078, quotient 



Divide 0.7438 by 12.9476. 

OPERATION". 

log 0.7438 . . . T.871456 
loiT 12.9476 . . . 1.112180 



2.759207 .-. 0.057447, quotient. 



Here, 1 taken from 1, gives 2 for a result. The sub- 
traction, as in this case, is always to be performed in the 
algebraic sense, 

3. To divide 0.06314 by .007241. 
log 0.06314 . . . 2.800305 
loir 0.007241 . . . 3.859799 



0.940506 .-. 8.7198, quotient. 



SEC. I.] LOGABITHMS. 19 

Here, 1 carried from the decimal part to the '6, changes 
it to 2, which being taken from 2, leaves for the char- 
acteristic. 

4. To divide 37.149 by 523.76. 

log 37.149 . . . 1.569947 
log 523.76 . . . 2.710133 

2.8.50814 .-. 0.0709274^ quotient 



5. Divide 37.149 bv 523.76. 



Ans. 0.0709274. 



The operation of division, particularly when combined with 
that of multiplication, can often be simplified by using the 
principle of 

AEITHiCETICAL COMPLEMENT. 

17. The Arithmetical Complement of a logarithm is the 
remainder obtained by subtracting it from 10. Thus, 8.130456 
is the arithmetical complement of 1.869544. The arithmetical 
complement of a logarithm may be written out ly commencing 
at the left hand and suUracting each figure from, 9, until the 
last significant figure is reached, which must he talcen from 10. 
The arithmetical complement is denoted by the symbol 
(a. c). 

Let a and h represent any two logarithms whatever, and 
a — b their difference. Since we may add 10 to, and sub- 
tract it from, a — h, without altering its value, we have, 

a -h = a ^ {10 -h) -10. . . . ( 10.) 

But, 10 — h is, by definition, the arithmetical complement 
of h: hence, Equation (10) shows that the difference between 
two logarithms is equal to the first, plus the arithmetical com- 
plernent of the second, minus 10. 



20 



ELEMENTS OF SUEYEYING. 



[book I. 



Hence, to divide one number by another by means of the 
arithmetical complement, vre have the following 

EuLE. — Fi/id the logarithm of the dividend, and the arith- 
metical complement of the logarithm of the divisor, add them 
together, and diminish the sum lyK); the numler corresponding 
to the resulting logarithm will be the quotient required. 

EXAMPLES. 

1. DiTide 32T.5 by 22.07. 

OPEEATION-. 

log 327.5 . . . 2.515211 
(a. c.) log 22.07 . . . S.65619S 



1.1TU09 .-. 14.839, quotient 



2. Divide 0.7438 by 12.9476. 

log 0.7438 . . . 1.871456 
(a. c.) log 12.9476 . . . S.887811 



2.759267 .-. 0.057447, quotient. 



In this example, the sum of the characteristics is 8, from 
which, taking 10, the remainder is 2. 



3. Divide 37.149 bv 523.76. 



log 37.149 . . 
(a. c.) log 523.76 . . 



1.569947 
7.280867 

2.850814 .-. 0.0709273, quotient 



4. Multiply 35S8S4 by 5672, and divide the product by 
89721. 



SEC. I.] 



LOGARITHMS. 



21 



log 358884 

log 5672 

(a. c.) log 89721 



OPERATIOK. 

. . 5.554954 
. . 3.753736 
. . 5.047106 



4.355796 



22688, result 



5. Find x in the proportion, 
3976 : 7952 : 



5903 



(a. c.) log 3976 
log 7952 
log 5903 

log X 



OPERATION. 

. . 6.400554 
. . 3.900476 
. . 3.771073 



4.072103 



X = 11806. 



The operation of subtracting 10 is always performed men- 
tally. 

XoTE 1. — In finding any term of a proportion by logarithms 
— obserye that, 

1. The sum of the logarithms of the extremes, is equal to the 
sum of the logarithms of the means : 

2. Tlie logarithm of the fourth term, is equal to the arith- 
metical cmnplement of the logarithm of the first term added to 
the logarithms of the mean terms: 

3. Tlie logarithm of either mean term, is equal to the arith- 
metical complement of the logarithm of the other mean added to 
the logarithms of the extremes, 

I^OTE 2. — If any proportion, as 

a \ I) '.'. c '. X, 
be changed into the form of an equation, thus, 

ax = Ic, tliQn 

(a. c.) log a + log I + log c — 10 = log x ; that is, 



22 



FT.E^fF.NTS OF SURYEYING. 



[BOOK I. 



The arithmetical compleme7it of the logarith?n of the multiplier of 
the unlcnown factor, ^;?«s the logarithms of the two other factors, 
minus 10, is equal to the logarithm of the unknown factor. 

KoTE 3. — If the logarithm, whose arithmetical complement 
is taken, exceeds 10, subtract it from 20, and reject 20 in the 
final operation. 

Eaising to Powers by Logarithms. 

18. To raise a number to any power. From the principle 
proved in (Art. 7), we have the following 

Rule. — Find the logaritlim of the numher, and multiply it 
hy the exponent of the power ; then find the numler correspond- 
ing to the resulting logaritlim^ and it will le the power required: 

EXAMPLES. 

1. rind the 5th power of 9. 

log 9 . . . 0.954243 



4.771215 



2. rind the 7th power of 



59049, power. 



Ans. 2097152. 



Extracting Eoots by Logarithms. 

19. To find any root of a number, from the principle 
proved in (Art. 8), we haye the following 

Rule. — Find the logarithm of tlie numler, and divide it ty 
the index of the root ; then find the number corresponding to 
the resulting logarithm, and it tcill be the root required. 

example. 

1. Find the cube root of 4096. 

The logarithm of 4096 is 3.612360, and one-third of this is 
1.204120. The corresponding number is 16, which is the root 
sought. 



sec: n.] GEOMETRICAL CONSTEUCTIOKS. 23 

SECTION n. 

GEOI^IETRICAL CONSTRUCTIONS. 

20. Before explaining the method of constructing geomet- 
rical problems, we shall describe some of the simpler instru- 
ments and their uses. 

DIVIDERS. 




21. The dividers is the most simple and useful of the 
instruments used for drawing. It consists of tw*o legs ha, Ic, 
which may be easily turned around a joint at t. 

One of the principal uses of this instrument is to lay off on 
a line, a distance equal to a given line. 

For example, to lay ofif on CD, a distance equal to AB. 

For this purpose, place the forefinger 
on the joint of the dividers, and set one ^ ' ' -^ 

foot at A: then extend, with the thumb ^| I ^ 

E 

and other fingers, the other leg of the 
dividers, until its foot reaches the point B. Then raise the 
dividers, place one foot at C, and mark with the other the 
distance CE : this will evidently be equal to AB, 

RULER AKD TRIANGLE. 

22. A Ruler of convenient size is about twenty inches in 
length, two inches wide, and a fifth of an inch in thickness. 



24 ELEMENTS OF SURVEYING. [BOOK I. 

It should be made of a hard material, perfectly straight and 
smooth. 

The hypothenuse of the right-angled triangle, which is used 
in connection with it, should be about ten inches in length, 
and it is most conyenient to have one of the sides considerably 
longer than the other. 





"We can solve, with the ruler and triangle, the two follow- 
ing problems. 

I. To draw through a given point a line which shall be parallel 
to a given line. 

23. Let C be tlie given point, and AB the given line. 

Place the hypothenuse of the triangle 

against the edge of the ruler, and then ' 

place the ruler and triangle on the paper, J^ B 

so that one of the sides of the triangle 

shall coincide exactly with A B : the triangle being below 

the line. 

Then, placing the thumb and fingers of the left hand 
firmly on the ruler, slide the triangle, with the other hand, 
along the ruler, until the side which coincided with AB reaches 
the point C. Leaving the thumb of the left hand on the ruler, 
extend the fingers upon the triangle and hold it firmly, and 
with the right hand, mark with a pen or pencil, a line through 
C: this line will be parallel to AB. 



SEC. n.] GEOMETEICAL CONSTEUCTIONS. 25 

n. To draw through a given point a line which shall be perpen- 
dicular to a given line. 

21. Let AB he the given line, and D the given point. 

Place the hypothennse of the triangle 
against the edge of the ruler, as before. 

Then place the ruler and triangle so that j 

one of the sides of the triangle shall coin- 
cide exactly with the line AB. Then slide the triangle along 
the ruler until the other side reaches the point D : then, draw 
through D, a right line, and it will be perpendicular to A B, 

SCALE OF EQUAL PAETS. 



I I 1 ! I I ' I I I L 



25. A scale of equal parts is formed by dividing a line of 
a given length, into equal portions. 

If, for example, the line ad, of a given length, say one 
inch, be divided into any number of equal parts, as 10, the 
scale thus formed is called a scale of ten parts to the inch. 
The line ab, which is divided, is called the ^cnit of the scale. 
This unit is laid off several times on the left of the divided 
line, and the points marked 1, 2, 3, &c. 

The unit of scales of equal parts is, in general, either an 
^ inch, or an exact part of an inch. If, for example, at, the 
unit of the scale, were half an inch, the scale would be one of 
10 parts to half an- inch, or of 20 parts to the inch. 

If it were required to take from the scale a line equal to 
two inches and six-tenths, place one foot of the dividers at 2, 
on the left, and extend the other to .6, which marks the sixth 
of the small divisions : the dividers will then embrace the 
required distance. 



26 



ELEMENTS OF SURVEYING. 



[BOOK I. 



DIAGONAL SCALE OF EQUAL PARTS. 



HJ' 







WW w 




03 


-^ UL / 




•08 


i9'_j 1 




■oi 


J_4_U 




.06 


1 / Tl 




05- 


M'-M / 




.04 


/MM// 




.03 


M N N / 1 




•02 


1 U 1 i f 




.0, 


il / / / / / 



a. I .2.3.^.5.6.7.8.9 k 



26. This scale is thus constructed. Take db for the unit 
of the scale, which may be one inch, J, i, or f of an inch, in 
length. On ab describe the square abed. Divide the sides ab 
and dc each into ten equal parts. Draw af, and the other nine 
parallels as in the figure. 

Produce ba^ to the left, and lay off the unit of the scale 
any convenient number of times, and mark the points 1, 2, 3, 
&c. Then, divide the line ad into ten equal parts, and through 
the points of division draw parallels to ab, as in the figure. 

Now, the small divisions of the line ab are each one -tenth 
(.1) of ab ; they are therefore .1 of ad, or .1 of ag or glu 

If we consider the triangle adf, we see, that the base df is 
one-tenth of ad, the unit of the scale. Since the distance 
from a to, the first horizontal line above ab is one-tenth of the 
distance ad, it follows that the distance measured on that line, 
between ad and af, is one-tenth of df: but since one-tenth of a 
tenth is a hundredth, it follows that this distance is one hun- 
dredth (.01) of the unit of the scale. A like distance measured 
on the second line is two hundredths (.02) of the unit of the 
scale; on the third, .03; on the fourth, .04, &c. 

If it were required to take, in the dividers, the unit of the 
scale, and any number of tenths, place one foot of the dividers 
at 1, and extend the other to that figure between a and b 
which designates the tenths. If two or more units are required, 



SEC. n.] 



GEOMETRICAL CONSTEUCTIONS. 



27 



the dividers must be placed on a point of division further to 
the left. 

When units, tenths, and hundredths are required, place 
one foot of the dividers where the vertical line through the 
point which designates the units, intersects the line which 
designates the hundredths: then, extend the dividers to that 
line between ad and he which designates the tenths: the dis- 
tance so embraced will be the one required. 

For example, to take off the distance 2.34, we place one 
foot of the dividers at Z, and extend the other to e: and to 
take off the distance 2.58, we place one foot of the dividers 
at ]) and extend the other to q, 

XoTE 1. — If a line is so long that the whole of it cannot 
be taken from the scale, it must be divided, and the parts of 
it taken from the scale in succession. 

XoTE 2. — If a line be given upon the paper, its length 
can be found by taking it in the dividers and applying it to 
the scale. 

SCALE OF CHORDS. 

J)30 jp 




27. If, with auy radius, as AC^ we describe the quadrant 
CD, and then divide it into 90 equal parts, each part is called 
a degree. 

If through C, and each point of division, a chord be drawn, 
and the lengths of these chords be accurately laid off on a 



28 



ELEMENTS OF SURVEYING. 



[book I. 



scale; such a scale is called a scale of chords. In the figure, 
the chords are drawn for every ten degrees. 

The scale of chords being once constructed, the radius of 
the circle from which the chords were obtained, is known; 
for, the chord marked 60, is always equal to the radius of 
the circle. A scale of chords is generally laid down on the 
scales which belong to cases of mathematical instruments, and 
is marked CHO. 

m. To lay off, at a given point of a line, with the scale of chords, 
an angle equal to a given angle. 

28. Let AB be the line, and A the given point. 

JTake from the scale the chord of 60 
degrees, and with this radius and the point 
^ as a centre, describe the arc BC. Then ^ 
take, from the scale, the chord of the given ^ 

angle, say 30 degrees, and with this distance as a radius, and B 
as a centre, describe an arc cutting BC in C. Through A and 
C, draw the line AC, and BAG will be the required angle. 

SEMICIECULAR PROTRACTOR. 
C 



0^- 





A B 

29. This instrument is used to lay down, or protract 
angles. It may also be used to measure angles included be- 
tween lines, already drawn upon paper. 



SEC. II.] 



GEOMETRICAL CONSTRUCTIONS. 



29 



It consists of a brass semicircle, ABC, divided to half de- 
grees. The degrees are numbered from to 180,, both ways; 
that is, from A to B and from B to A, The divisions, in the 
figure, are made only to degrees. There is a small notch at 
the middle of the diameter AB, which indicates the centre of 
the protractor. 

IV. To lay ofif an angle with a Protractor. 

30. Place the diameter AB on the line, so that the centre 
shall fall on the angular point. Then count the degrees con- 
tained in the given angle, from A toward B, or from B toward 
Ay and mark the extremity of the aiO with a pin. Eemove 
the protractor, and draw a line through the point so marked, 
and the angular point: this line will make with the given line 
the required angle. 

SECTORAL SCALE OF EQUAL PARTS. 




31. The sector is an instrument generally made of ivory or 
Irass. It consists of two arms, or sides, which open, by turning 
round a joint, at their common extremity. 

There are several scales laid down on the sector : those, how- 
ever, which are chiefly used in drawing lines and angles, are, 
the scale of chords already described, and the scale of equal 
parts now to be exj^lained. 

On each arm of the sector, there is a diagonal line that 
passes through the point about which the arms turn : these 
diagonal lines are divided into equal parts. 



30 ELEMENTS OF SURVEYING. [BOOK I. 

On the sectors which belong to the cases of English instru- 
ments, the diagonal lines are designated by the letter L, and 
numbered from the centre of the sector, 1, 2, 3, 4, 5, 6, 7, 8, 
9, 10, to the two extremities. On the sectors which belong to 
cases of French instruments, they are designated, "Les parties 
egales," and numbered 10, 20, 30, 40, &c., to 200. On the Eng- 
lish sectors there are 20 equal divisions between any two of 
the lines numbered 1, 2, 3, &c., so that there are 200 equal 
parts on the scale. 

The advantage of the sectoral scale of equal parts, is this : 

Let it be proposed to draw a line upon paper, on such a 
scale that any number of parts of the line, 40 for example, shall 
be represented by one inch on the paper, or by any part of an 
inch. Take the inch, or part of the inch, from the scale of inches, 
on the sector ; then, placing one foot of the dividers at 40, on 
one arm of the sector, open the sector until the other foot 
reaches to the corresponding number on the other arm: then, 
lay the sector on the table without varying the angle. 

Now, if we regard the lines on the sector as the two sides of 
a triangle, of which the line 40, measured across, is the base, it 
is plain, that if any other line be likewise measured across the 
angle of the sector, the bases of the triangles, so formed, will be 
proportional to their sides. Therefore, if we extend the dividers 
from 50 to 50, this distance will represent a line of 50, to the 
given scale: and similarly for other lines. 

V. Required to lay down a line of sixty-seven feet, to a scale of 
twenty feet to the inch. 

Take one inch from the scale of inches : then place one foot 
of the dividers at the twentieth division, and open the sector 
until the dividers will just reach the twentieth division on the 
other arm: the sector is then set to the proper angle; after 
which the required distance to be laid down on the paper is 



SEC. n.] 



GEOMETRICAL CONSTRUCTIONS. 



31 



found by extending tlie dividers from the sixty-seventh division 
on one arm, to the sixty-seventh' division on the other. 

gutter's scale. 

32. This is a scale of two feet in length, on the faces of 
which several scales are marked. The face on which the divi- 
sions of inches are made, contains, however, all the scales neces- 
sary for laying down lines and angles. These are, the scale of 
equal parts, the diagonal scale of equal parts, and the scale of 
chords, all of which have been described. 

SOLTJTIOi^ OF PROBLEMS. 

I. At a given point, in a given straight line, to erect a perpendicular 

to the line. 

33. Let A be the given point, and BC the given line. 

From A, lay off any two distances, AB 
and A C, equal to each other. . Then, from 
the points JB and C, as centres, with a 
radius greater than BA, describe two arcs — 
intersecting each other at D : draw AD, and 
it will be the perpendicular required. 



D 



n. From a given point, without a straight line, to let fall a perpen- 
dicular on the line. 

34. Let A be the given point, and BD the given line. 

From the point A, as a centre, with a 
radius sufficiently great, describe an arc 
cutting the line BJ) in the two points B 
and J) : then, mark a point ^, equally dis- 
tant from the points JEJ and B, and draw 
AU: AE will be the perpendicular required. 




32 ELEMENTS OF SURTEYING. [BOOK I. 

m. At a point, in a given line, to make an angle equal to a 
given angle. 

35. Let A be tlie given point, AU the given line, and IKL 
the given angle. 

From the vertex K, as a centre, with ^ ^ 

any radius, describe the arc IL, termi- y^ 
nating in the two sides of the angle. ^ I J" 

From the point A, as a centre, with a distance AE, eqnal to 
KI, describe the arc ED ; then take the chord LI, with which, 
from the point ^ as a centre, describe an arc cutting the 
indefinite arc DE, in D ; draw AD, and the angle EAD will 
be equal to the given angle K. 

TV. To divide a given angle, or a given arc, into two equal parts. 

36. Let A CB be the given angle, and AEB the arc which 
measures it. ^ 

From the points A and B as centres, ^ 
describe, with the same radius, two arcs 
cutting each other in J>; through D and v/ 

the centre C draw CD : the angle A CE ^ 

will be equal to the angle ECB, and the arc AE to the 
arc EB. 

V. Through a given point, to draw a parallel to a given line. 

37. Let A be the given point, and B C the given line. 

From ol as a centre, with a radius 

-A* p 

greater than the shortest distance from B-\ ^^\^ 

A to BC, describe the indefinite arc \ ^,.-'''' \ 

ED. Then, from the point E as a ^^ ' ^ 

centre, with the same radius, describe the arc AF; make EB 

= AF, and draw AB : thon will AB be the parallel required. 




SEC. II.] GEOMETRICAL CONSTEUCTIOXS. 33 

VI. Two angles of a triangle being given, to find the third. 

38. Draw tlie indefinite line DEF. q ^ 

At the point E, make the angle DEC 
equal to one of the given angles, and 



T) J? TP 

the angle CEH equal to the other: 

the remaining angle REE will be the third angle required. 



Vn. To represent, on paper, a line of a given length, so that any num- 
ber of its parts shall correspond to the unit of the scale. 

39. Suppose that the given line were 75 feet in length, 
and it were required to draw it on paper, on a scale of 25 
feet to the inch. 

The length of the line, 75 feet, being divided by 25, will 
give 3, the number of inches which will represent the line on 
paper. 

Therefore, di'aw the indefinite line AB, on which lay off 



from C, a distance A C equal to 3 inches : A C will represent 
the given line of 75 feet, drawn to the required scale. 

XoTE. — This problem explains the manner of representing 
a line upon paper, so that a given number of its parts shall, 
correspond to the unit of the scale, whether that unit be an. 
inch or any part of an inch. 

When the length of the line to be laid down is given, and 
it has been determined how many parts of it are to be repre- 
sented on the paper by a distance equal to the unit of the 
scale, we find the length which is to be taken from the scale 
by the following 

EuLE. — Divide the length of the line ly the nnmler of jimrts 
which is to ie represented ly the unit of the scale: the quotient 
will shoio the niimler of units which is to be taken from the scale. 



34: ELEMENTS OF SURVEYING. [BOOK I. 

E X A 31 P L E S. 

1. If a line of 640 feet is to be laid do^vn on paper, on a 
scale of 40 feet to the incli; what length must be taken from 
the scale? 40) 640 (16 inches. 

2. If a line of 357 feet is to be laid down on a scale of 
68 feet to the unit of the scale (which we will suppose half an 

inch), how many parts are to be taken? 

. j 5.25 parts, or 
( 2.625 inches. 

3. A line of 384 feet is di'awn on paper, on a scale of 45 
feet to the inch ; what is its length on the paper ? 

A71.S. 8.53 inches. 

!N"OTE. — When the length of a line on the paper is given, 
and it is required to find the true length of the line which it 
represents, take the line in the dividers and apply it to the 
scale, and note the number of tmits, and parts of a unit, to 
which it is equal. Then multiply this number by the number 
of parts which the unit of the scale represents, and the product 
will be the length of the line. 

For example, suppose the length of a line drawn on the 
paper was found to be 3.55 inches, the scale being 40 feet to 
the inch : then, 

3.55 X 40 = 142 feet, the length of the line. 

VUL Having given two sides and the included angle of a triangle, 
to describe the triangle. 

40. Let the line J3 = 150 feet, and C = 120 feet, be the 
given sides ; and A = 30 degrees, the given angle : to describe 
the triangle on a scale of 200 feet to the inch. 

Draw the indefinite line DG, and at the point D, make the 



SEC. n.] 



GEOMETKICAL CONSTEUCTIONS. 



35 





:i:igle GDII equal to 30 degrees: then 
luy of£ DG equal to 150 feet, equal to 
three-quarters of an inch, and DH 
equal to 120 feet, equal to six-tenths of 
an inch, and draw GH : then, DHG 
will he the required triangle. 



IX. The three sides of a triangle being given, to descrihe the 
triangle. 

41. Let A, B and C be the sides. 
^Make DE equal to the side A. 

From the point Z> as a centre, with a 

radius equal to the second side B, 

describe an arc : from E as a centre, 

with a radius equal to the third side 

C, describe another arc, intersecting the former in F ; draw DF 

and EF, and DFE will be the triangle required. 

X. Having given two sides of a triangle and an angle opposite one 
of them, to describe the triangle. 

42. Let A and B be the giyen sides, and C the given angle, 
which we will suppose to be opposite the side B. 

Draw the indefinite line DF: then, 
at any point of it, as D, make the 
angle FDE equal to the angle C : take 
DE = A, and from the point E, as a 
centre, with a radius equal to the other 
given side, B, describe an arc, cutting DF in F; draw EF: 
will DEE be the required triangle. 

If the angle C is acute, and the 
side B less than A, then the arc 
described from the centre E with 
the radius EF = B will cut the 
side DF in two poiuts, F and G, 




then 




36 ELEMENTS OF SURVEYING. [BOOK I. 

lying on the same side of D : hence, there will be two triangles, 
DEF and DEG, either of which will satisfy all the conditions 
of the problem. 



XI. The adjacent sides of a parallelogram, with the angle which 
they contain, being given, to describe the parallelogram. 

43. Let A and B be the given sides, and G the given angle. 

Draw the line DH, and lay off DE 
equal to A ; at the point D, make the / /; ■' 

angle EDF =. G; take DF^ B: de- ^Z ^ 

scribe two arcs, the one from F, as A 1 / 

J§) < ^ — 



a centre, with a radius FG = A, the 
other from E, as a centre, with a radius EG = BF ; through 
the point G, where these arcs intersect each other, draw FG, 
EG : then, DEGF will be the parallelogram required. 

XII. To find the centre of a given circle, or arc. 

44. Take three points, A, By C, anywhere in the circum- 
ference, or in the arc : draw AB, BG ; 
bisect these two lines by the perpen- 
diculars, BE, FG : the point 0, where 
these perpendiculars meet, will be the 
centre sought. i^ 

A similar construction serves for 
making a circumference pass through three given points. A, B, 0, 
and also for describing a circumference, about a given triangle. 

For, if we join the points by the straight lines AB, BG, 
and AC, and bisect either two of them, by perpendiculars, 
their point of intersection, 0, will be the centre of the required 
circle. 




SEC. in.] PLANE TRIGONOMETRY. 37 

SECTION III. 

PLANE TRIGONOMETRY. 

45. Plane Trigonometry is that branch of Mathematics 
which treats of the solution of plane triangles. 

In every plane triangle there are six parts: three sides and 
thi^ee angles. When three of these parts are given, one being a 
side, the remaining parts may be found by computation. 

46. An angle is measured by the arc of a circle included 
between its sides, the centre of the circle being at the vertex, 
and its radius being equal to 1. 

47. If two lines be drawn through the centre of a circle, 
at right angles to each other, they will divide the circum- 
ference into four equal parts, each of which is called a 
quadrant. 

For convenience, the quadrant is divided into 90 equal parts, 
each of which is called a degree; each degree into 60 equal 
parts, called minutes; and each minute into 60 equal parts, 
called seconds. Degrees, minutes, and seconds, are denoted by 
the symbols °, ', ". Thus, the expression T 22' 33", is read, 
7 degrees, 22 minutes, and 33 seconds. 

A quadrant contains 324,000 seconds, and an arc of 7° 22' 33" 
contains 26,553 seconds; and any arc of a quadrant may be 
expressed in seconds. 

48. The com^ilement of an arc is what remains after sub- 
tracting the arc from 90°. Thus, the arc EB is the comple- 
ment of AB. 



38 



ELEMENTS OF SUEYETING. 



[book I. 




49. The siq)j>Iej7ient of au arc is what 
remains after subtracting the arc from 
180^ Thus, GJ^ is the supplement of 
the arc ABF. 

50. The si7ie of an arc is the per- 
pendicular let fall from one extremity of 
the arc on the diameter which passes 
through the other extremity. Thus, JBD 
is the sine of the arc A^. 

51. The cosine of an arc is the part of the diameter inter- 
cepted between the foot of the sine and centre. Thus, OD is 
the cosine of the arc AJB. 

52. The tangent of an arc is the line which touches it at 
one extremity, and limited by a line drawn through the other 
extremity and the centre of the circle. Thus, A C is the tan- 
gent of the arc AJy. 

5Z. The seccmt of an arc is the line drawn from the centre 
of the circle through one extremity of the arc, and limited 
by the tangent passing through the other extremity. Thus, 
OC is the secant of the arc AJj. 

54. The four lines, JBD, OB, AC, OC, depend for their 
Yalues on the arc AB and the radius OA ; they are thus 
written : 

For BB, we write sin AB 

For OD " " cos AB 

For .4 C " '• tan AB 

For 0(7 '-' « sec AB 

55. If ABE be a quadrant, or 90°, then EB will be the 
complement of AB. Let the lines ET and IB be drawn per- 
pendicular to OE, Then, 



SEC. m.] 



PLANE TRIGONOMETRY. 



89 



ET, the tangent of EB, is called tlie cotangent oi AB ; 
IB, the sine of EB, is the cosine of AB ; 
OT, the secant of EB, is the cosecant of AB. 

In general, if A is any arc or angle, T\'e have, 

cos A = sin (90° - A) 
cot A = tan (90=^ - A) 
cosec A = sec (90° — A) 

56. If we take an arc, ABEF, 
greater than 90°, its sine will be Fff; 
OR will be its cosine ; ^ § its tangent, 
and OQ its secant. But FR is the 
sine of the arc GF, which is the sup- 
plement of ^i^, and OH is its cosine; 
hence, tJie sine of an arc is equal to 
the sine of its siqji^lement ; and tlie 
cosine of an arc is equal to the cosine of its siqyple^nent.^ 

Furthermore, AQ is the tangent of the arc AF, and OQ is 
its secant : GL is the tangent, and OL the secant of the sup- 
plemental arc GF. But since AQ is equal to GL, and OQ to 
OL, it follows that, the tangent of an arc is equal to the tangent 
of its supplement; and the secant of an arc is equal to the secant 
of its suppletnent.^ 




Table of Natural Sines. 

57. A ]SrATURAL SiXE, COSIXE, TaXCtE2>"T, or COTA^'GEXT. 

is the sine, cosine, tangent, or cotangent of an arc whose 
radius is 1. 

A Table of Xatural Sixes is, therefore, a table showing 
the values of the sines, cosines, tangents, and cotangents of all 



* These relations are between the numerical rallies of the trigonometrical lines; the 
algebraic signs, -which they have in the diflferent quadrants, are not considered. 



40 ELEMENTS OF SUR\^YING. [BOOK I. 

the arcs of a quadrant, diyided either to minutes or seconds. 
The Table of Natural Sines, beginning at page 63, of the tables, 
shoAvs the values of the sines and cosines only. 

Table of Logaeithmic Sines. 

58. In this table are arranged the logarithms of the nu- 
merical values of the sines, cosines, tangents, and cotangents 
of all the arcs of a quadrant, calculated to a radius of 
10,000,000,000. The logarithm of this radius is 10. In the 
first and last horizontal lines of each page, are written the 
degrees whose sines, cosines, &c., are expressed on the page. The 
vertical columns on the left and right are columns of minutes. 

To find, in the table, the logarithmic sine, cosine, tangent, or 
cotangent of any given angle. 

59. If the angle is less than 45°, look for the degrees in 
the first horizontal line of the difierent pages : when the degrees 
are found, descend along the column of minutes, on the left 
of the page, till you reach the number showing the minutes: 
then pass along a horizontal line till you come into the column 
designated, sine, cosine, tangent, or cotangent, as the case may 
be: the number so indicated is the logarithm sought. Thus, 
on page 37, for 19° 55', we find, 

sine 19° 55' 9.532312 

cos 19° 55' • . . 9.973215 

tan 19° 55' 9.559097 

cot 19° 55' 10.440903 

If the angle is greater than 45°, search for the degrees along 
the bottom line of the different pages: when the number is 
found, ascend along the column of minutes on the right-hand 
side of the page, till you reach the number expressing the 
minutes: then pass along a horizontal line into the column 



SEC. III.] TUCsE TPJG0X0:5IETRY. 41 

designated tang, cot, sine, or cosine, as the case may be: the 
nnmber so pointed out is the logarithm required. 

60. The cohimn designated sine, at the top of the page, is 
designated by cosine at the bottom: the one designated tang, 
by cotang, and the one designated cotang, by tang. 

The angle found by taking the degrees at the top of the 
page, and the minutes from the left-hand vertical column, is 
the complement of the angle found by taking the degi'ees at 
the bottom of the page, and the minutes from the right-hand 
column on the same horizontal line with the first. Therefore, 
sine, at the top of the page, should correspond with cosine, at 
the bottom; cosine "with sine, tang with cotang, and cotang 
with tang, as in the tables. 

If the augle is greater than 90^, we have only to subtract 
it from 180°, and take the sine, cosine, tangent, or cotangent 
of the remainder, or supplement. 

Column of Diflferences. 

61. The column of the table next to the column of sines, 
and on the right of it, is designated by the letter D. This 
column is calculated in the following manner : 

Opening the table at any page, as 4,2, the sine of 24:° is 
found to be 9.609313; that of 24° 1', 9.609597: their difference 
is 284; this being divided by 60, the number of seconds in a 
minute, gives 4.T3, which is entered in the column D. 

Xow, supposing the increase of the logarithmic sine to be 
proportional to the increase of the arc, and it is nearly so 
for 60", it follows, that 4.73 is the increase of the sine for 1". 
Similarly, if the arc were 24° 20', the increase of the sine for 
1" would be 4.65. 

The same remarks are applicable in respect of the column 
D, after the column cosine, and of the column D, between the 



42 ELEMENTS OF SURVEYING. [BOOK I. 

tangents and cotangents. The column D, between the columns 
tangeuts and cotangents, answers to both of these columns. 

Xow, if it were required to find the logarithmic sine of an 
arc expressed in degrees, minutes, and seconds, we have only to 
find the degrees and minutes as before ; then, multiply the cor- 
responding tabular difference by the seconds, and add the product 
to the number first found, for the sine of the given arc. 

Thus, if we T^ish the sine of 40^ 26' 28". 

The sine 40° 2G' 9.811952 

Tabular difference 2.47 .... 
^s'umber of seconds 28 .... 

Product . . 69.16 to be added, 69.16 

Gives for the sine of 40° 26' 28", 9.812021. 

The decimal figures at the right are generally omitted in 
the last result; but when they exceed five-tenths, the figure 
on the left of the decimal point is increased by 1 ; the loga- 
rithm obtained is then exact, to within less than one unit of 
its right-hand place. 

The tansrent of an arc. in which there are seconds, is found 
in a manner entirely similar. In regard to the cosine and 
cotangent, it must be remembered, that they increase while the 
arcs decrease, and decrease as the arcs are increased; conse- 
quently, the proportional numbers found for the seconds, must 
be subtracted, not added. 

EXA:^rPLES. 

1. To find the cosine of 3° 40' 40". 

The cosine of 3° 40' 9.999110 

Tabular difference .13 

I^umber of seconds 40 

Product . . 5.20 to be subtracted, 5.20 

Gives for the cosine of 3° 40' 40" . . 9.999105. 



SEC. in.] PLANE TRIGONOMETEY. 43 

2. Find the tangent of 37^ 28' 31". A^is. 9.884592. 

3. Find the cotangent of ST 57' 59". Ans. 8.550356. 

To find the degrees, minutes, and seconds answering to any given 
logarithmic sign, cosine, tangent, or cotangent. 

62. Search in the table, in the proper colunin, and if the 
number is found exactly, the degrees will be shown either at 
the top or bottom of the page, and the minutes in the side 
column, either at the left, or right. 

But, if the number cannot be found in the table, take from 
the table the degrees and minutes answering to the nearest 
less logarithm, the logarithm itself, and also the corresponding 
tabular difference. Subtract the logarithm taken from the table 
from' the given logarithm, annex two ciphers to the remainder, 
and then diyide the remainder by the tabular difference : the 
quotient will be seconds, and is to be connected with the 
degrees and minutes before found : to be added for the sine 
and tangent, and suUracted for the cosine and cotangent. 

EXAMPLES. 

1. Find the arc answering to the sine 9.880054 
Sine 49° 20', next less in the table 9.879963 



Tabular difference ..... 1.81) 91.0jO (50". 

# 

Hence, the arc 49° 20' 50" corresponds to the giyen 

si ire 9.880054. 

2. Find the arc whose cotangent is . 10.008688 
cot 44° 26', next less in the table 10.008591 

Tabular difference 4.21) 97.00 (23". 

■ Hence, 44° 26' - 23" = 44° 25' 37" is the arc answering to 
the giyen cotangent, 10.008688. 



4^4 ELEMENTS OF SURVEYING. [BOOK I. 

3. Find the arc answering to tangent, 9.979110. 

A?is. 43° 37' 21". 

4. Pind the arc answering to cosine, 9.944599. 

A71S. 28° 19' 45". 



THEOREM I. 

The sides of a 2^^ctne triangle are proportional to the sines of 
their opposite angles. 

63. Let ABC be a triangle; then will 

CB : (7^ : : sin ^ : sin B, 

For, with ^ as a centre, and A J) equal to the less side BC, 
as a radins, describe the arc JDI: and o 

with ^ as a centre and the equal radius 
B G, describe the arc CL, and draw JDJE ^ 

and CF perpendicular to AB : now BE 
is the sine of the ^ angle A, and CF is the sine of B, to the 
same radius AB or B C. But by similar triangles, 

AD : DE '.: AO : CF. 

But AB being equal to BC, we have 

BC : sin yl : : AC : sin B, or 
BC : AC :: sin A : sin B. 

By comparing the sides AB, AC, in a similar manner, we 
should find, 

AB : AC :: sin C : sin B. 

THEOREM II. 

Li any triangle, tlie sum of the tico sides containing either 
angle, is to their differeiice, as the tangent of half the sum of 
the tivo other a?igles, to the tangent of half their difference. 




SEC. III.] 



PLANE TEIGONOMETEY. 



45 




64. Let A GB be a triangle : then will 
AB ^ AC \ AB - AC : : tan \{C + B) : tan ^{C - B), 

"With ^ as a centre, and a radius 
A C, the less of the two given sides, 
let the semicircumference IFCJE be 
described, meeting AB in I, and BA 
produced, in M Then, BE will be 
the sum of the sides, and BI their 
difference. Draw CI and AF. 

Since CAE is an outward angle of the triangle A CB, it is 
equal to the sum of the inward angles C and B (Bk. I., Prop. 
XXV., Oor. 6). But the angle CIE being at the circumference, 
is half the angle CAE at the centre (Bk. III., Prop. XVIII.) ; 
that is, half the sum of the angles C and B, or equal to 
^{C + B). 

The angle ^i^C = ACB, is also equal to ABC + BAF; 
therefore, BAF = ACB - ABC 

But, ICF=z i {BAF) =i{ACB-ABC), ov i{C- B). 

With I and C as centres, and the common radius IC, let 
the arcs CJD and Z6r be described, and draw the lines CE Mid. 
IH perpendicular to IC, The perpendicular CE will pass 
through E, the extremity of the diameter IE, since the right 
angle ICE must be inscribed in a semicircle. 

But CE is the tangent of CIE =. i{C + B); and III is 
the tangent of ICB = ^ {C — B), to the common radius CI 

But since the lines CE and IIT are parallel, the triangles 
BCE and BUI are similar, and give the proportion, 

BE : BI '.'. CE : IH, or 

by placing for BE and BI, CE and IH, their values, we have, 

AB-\-AC: AB--AC:: tan i{C + B) : tan HC-B). 



46 



ELEMENTS OF SUBVEYING. 



[book I. 



THEGEEM III. 

In any plane triangle, if a line is drawn from the vertical 
angle perjoendicular to the base, dividing it into tzvo segments : 
then, the luhole lase, or sum of the segments, is to the sum of 
the other two sides, as the difference of those sides, to the differ- 
ence of the segments. 

65. Let BAC be a triangle, and AD perpendicnlar to tlie 
base BC ; then will 

BC : CA + AB :: CA — AB 

For, AB^ = in? + ZO^ (Bk. IV., 
Prop. XI.) ; and JC^ = X>6'^ + Alf- 
by subtraction, 

-JC^ _ AB^ ^ 6^ _ BD^, n 7) 

But, since tlie difference of the squares of two lines is 
equal to the rectangle contained by their sum and difference 
(Leg., Bk. lY., Prop. X.), we haye, 

~AC^ - AB" = {AC + AB) .{AC- AB) 
and -(JW - 'DB^ = {CD + BB) . {CD - DB) 

therefore, {CD + DB) . {CD - DB) = {AC+ AB) . {AC- AB) 
hence, CD + DB : AC + AB :: AC - AB : CD - DB. 




THEOREil IT. 

Tn any right-angled ^lane triangle, radius is to the tangent 
of eitlier of the acute angles, as the side adjacent to the side 
opposite. 

66. Let CAB be the proposed triangle, and denote the radius 
by R : then will 

R : ioxiC '.: AC : AB. 

For, with any radius as CD, describe 
the arc DH, and draw the tangent DC. 




SEC. III.] PLANE TEIGONOMETEY. 47 

Prom the similar triangles CDG and CAB, wc have, 

CD : DG :: CA : AB; lience, 
R : tan C :: CA : AB. 

By describing an arc, with ^ as a centre, we could show in 
the same manner that, 

E : tsin B :: AB : AC. 

THEOREM Y. 

1)1 every rigid-angled plane triangle, radius is to tlie cosine 
of either of the acute angles, as the hy2)othemcse to the side 
adjacent. 

67. Let ABC be a triangle, right-angled at B: then will 

B : QO^ A :: AC : AB. 
For, from the point A as a centre, 
with any radius as AB, describe the arc 
DF, which will measure the angle A ; and 
draw BJS perpendicular to AB : then will ^^ JS'F 
AE be the cosine of ^. 

The triangles ABE and A CB, being similar, we have, 
AB : AE '.: AC : AB ; that is, 
R '. co^ A :. AC : AB. 

General Principles. 

68. The relations between the sides and angles of plane 
triangles, demonstrated in these five theorems, are sufficient to 
solve all the cases of Plane Trigonometry. Of the six parts, 
which make up a plane triangle, three must be given, and at 
least one of these a side, before the others can be determined. 

If the three angles only are given, it is plain, that an in- 
definite number of similar triangles may be constructed, the 




48 ELEMENTS OF SUETEYrN'G. [BOOK I. 

angles of which may be respectively equal to the angles that 
are given, and therefore, the sides could not be determined. 

Assuming, with this restriction, any three parts of a triangle, 
as given, one of the four following cases, will always be pre- 
sented. 

I. "\Vhen two angles and a side are given. 
II. TVhen two sides and an opposite angle are given. 

III. TTlien two sides and the included angle are given. 

IV. When the three sides are given. 

CASE I. 

69. When two angles and a side are given. 

1. In a plane triangle, ABC, there are given the angle 
A = 58° 07', the angle B = 22^ 3T', and the side AB = c = 408 
yards; to final C, a and ^.* 

GEO AIETEIC ALLY. 

Draw an indefinite straight line, AB, 
and from the scale of equal parts lay off 

AB equal to 408. Then at A, lay off an -^^ » ^^^^^ 

angle equal to 58° 07', and at B an angle equal to 22° 37', and 
draw the lines AC and BC : then wiU ABC be the triangle. 

The angle C may be measured either with the protractor 
or the scale of chords, and will be equal to 99° 16'. The sides 
AC and BC may be measured by referring them to the scale of 
equal parts. We shaU find .46' = 158.9 and ^C'=351 yards. 

TKIGOXOMETEICALLT. 

Add the given angles together, and subtract their sum from 
180 degrees. The remaining parts of the triangle can then be 
found by Theorem I. 

* The sides lying opposite the angles A, B and C. arc denoted by a, b and c. 




SEC. in.] PLANE TRIGONOMETRY. 49 



To the ano^le A = oS° 



O A*' 



add the angle ^ = 22° 37' 

their sum , .... -. = 80° 44' 
taken from 180° 00' 

leaves C 99° 16', of which, 

as it exceeds 90°, we use the supplement 80° 44'. 

To find BC = a. 

From Theorem I., we have, 

sin (7 : sin J. : : c : a. 

Applying logarithms, we have, 

(a. c.) log sin C (99° 16') 0.005705 

log sin A (58° 07') 9.928972 

log c (408) 2.610660 

log a 351.024 2.545337 

In like manner, 

sin C : sin j5 : : c : d. 

Applying logarithms, we have, 

(a. c.) log sin C (99" 16') 0.005705 

log sin B (22° 37') 9.584968 

log c (408) 2.610660 

log b 158.976 2.201333 

A71S. C = 98° 16', a = 351.024, and d = 158.976. 

KoTE. — The logarithm of the fourth term of a proportion 
is obtained by adding the logarithm of the second term to that 
of the third, and subtracting from their sum the logarithm 
of the first term. But to subtract the first term is the same 
as to add its arithmetical complement and reject 10 from the 



50 ELEMENTS OF SURVEYING. [BOOK I. 

Slim (Sec. I., Art. 17) : hence, the arithmetical complement of 
the first term added to the logarithms of the second and third 
terms, minus ten, will give the logarithm of the fourth term. 

2. In a triangle ABC, there are given A = 38° 25', B = 
57° 42', and c = 400 : required the remaining parts. 

Ans, C = 83° 53', a = 249.974, h = 340.04. 

CASE II. 
70. When two sides and an opposite angle are given. 

In a plane triangle, ABC, there are given AC = b =^ 216, 
CB = a = 117, the angle A = 22° 37', to find the other parts. 

GEOMETRICALLY. 

Draw an indefinite right line ABB' : 
from any point, as A, draw AC, making 
BAC = 22° 37', and make AC = 216. ,, , . . 
With G as a centre, and a radius equal 
to 117, the other given side, describe the arc B'B ; draw CB 
and CB' ; then will either of the triangles ACB or ACB', 
answer all the conditions of the question. 

TEIGOXOMETEICALLY. 

From Theorem I., we have, 

a : b : : sin ^ : sin ^ 
By applying logarithms, we have, 

(a. c.) log a (lir) ..."... 7.931814 

log b (216) 2.334454 

log sin A (22° 37') .... 9.584968 

log sin B, 45° 13' 55", or 134° 46' 05" . 9.851236 

The ambiguity in this, and similar examples, arises in 
consequence of the first proportion being true for either of the 
ano-les ABC, or AB'C, which are supplements of each other, 




SEC. m.] PLANE TEIGONOMETBY. 51 

aiid therefore, have the same sine (Art. 56). So long as the 
two triangles ACB and ACB' exist, the ambiguity will con- 
tiune. But if the side CB, opposite the given angle, is greater 
than AC, the arc BB' will cut the line ABB', on the same 
side of the point A, in but one point, and then there will be 
only one triangle answering to the conditions. 

If the side CB is equal to the perpendicular Cd, the arc BB' 
will be tangent to ABB', and in this case also, there will be 
but one triangle. TThen CB is less than the perpendicular Cd, 
the arc BB' will not intersect the base ABB', and in that case 
no triangle can be formed, or it will he impossible to fulfil the 
conditions of the problem. 

In the example under consideration, there are two solutions, 
the first corresponding to B' = 45° 13' 55", and the second to 
ABC = 134° 46' 05". 

First case. 

A 22° 37' 

B' 45° 13' 55" 

O 180° - 67° 50' 55" = 112° 09' 05". 



Thus, in the triangle ACB', 

sin B' : sin C : : l : c, 

and applying logarithms, 

(a. c.) log sin B' (45° 13' 55") .... 0.148764 
log sin C (112° 09' 05") .... 9.966700 
log b (216) 2.334454 

log c 281.785 2.449918 

Second case, 

A 22° 37' 

B 134° 46' 05" 



(7 ...... . 180° - 157° 23' 05" = 22" 36' 55". 



52 ELEMENTS OP SURVEYING. [BOOK I. 

Thus, in the triangle ACB, 

sin B \ m\ C '. h : c. 
and applying logarithms, 

(a. c.) log sin B (134° 46' 05") . . . 0.148764 
log sin C (22° 36' 55") . . . 9.584943 
log 1) (216) 2.334454 

log c 116.993 2.068161 

2. Given two sides of a triangle, 50 and 40 respective]y, 
and the angle opposite the latter, equal to 32° : required the 
remaining parts of the triangle. 

A71S. If the angle opposite the side 50 is acute, it is equal 
to 41° 28' 59"; the third angle is then equal to 106° 31' 01", 
and the third side to 72.368. If the angle opposite the side 
50 is obtuse, it is equal to 138° 31' 01", the third angle to 
9° 28' 59", and the remaining side to 12.436. 

CASE III. 
71. When two sides and their included angle are given. 

Let ABC be a triangle; AB and BC, ^ 

the given sides, and B the given augle. 

Since B is known, we can find the 
sum of the two other angles: for, j^- — ' h 

A -[- C = 180° — B, and 
^{A-\-0)=l (180^ - B). 

We next find half the difference of the angles A and C, 
by Theorem IL, viz., 

B0+ BA : BC- BA : : tan i {A + C) : tan i{A- C), 

in wliich we consider BC greater than BA, and therefore A is 
greater than C ; since the greater angle must be opposite the 
greater side. 




SEC. III.] 



PLANE TRIGONOMETRY. 



63 



Having found half the difference of A and C, by adding 

it to the half sum, -J (yl + (7), we obtain the greater angle, 

and by subtracting it from half the sum, we obtain the less. 

That is, 

i{A -\-C) + i{A-C) =A, and 

i{A +C) -i{A^C) = a 

Having found the angles A and (7, the third side A C may 
be found by the proportion, 

sin A : sin B : : a : b. 

EXAMPLES. 

1. In the triangle ABC, let BC = 540, AB = 450, and the 
included angle B = 80° : required the remaining parts. 

GEOMETEICALLT. 

Draw an indefinite right line BO, and from any i>oint, 
as B, lay off a distance BC = 540. At B make the angle 
CBA = 80° : draw BA, and make the distance BA = 450 ; 
draw AC; then will ABC be the required triangle. 

TRIGONOMETRIC ALLY. 

BC +BA = 540 + 450 = 990; and BC- BA = 540 - 450 = 90. 
A + C= 180° - B = 180° - '80° = 100°, and therefore, 
^{A+C)=i (100°) = 50°. 



To find i (a — O). 
By Theorem 11. , we have, 
BC + BA : BC-BA :: tani{A + C) : tan l(^-C). 
Applying logarithms, we have, 

(a. c.) log (BC + BA) (990) . . . 7.004365 
log (BC - BA) (90) . . . 1.954243 
log tan i (^ + (7) 50° . . . 10.076187 
log tan i (A - C) 6° 11' . . 9.034795 



54 ELEMENTS OF SURVEYING. [BOOK I. 

Hence, 50^ + 6° 11' = 5G" 11' = A; and 50" - 6° 11' = 
43° 49' = a 

To find the third side AO. 
sin C : sin ^ : : c : b. 
Applying logarithms, we have, 

(a. c.) log sin C (43° 49') 0.159672 

log sin B (80°) 9.993351 

log c (450) 2.653213 

log i 640.082 2.806236 

2. Given two sides of a plane triangle, 1686 and 960, and 
their included angle 128° 04': required the other parts. 

Ans. Angles, 33° 34' 39"; 18° 21' 21"; side 2400. 

CASE IV. 

72. Having given the three sides of a plane triangle to find 
the angles. 

Let fall a perpendicular from the angle opposite the greater 
side, dividing the given triangle into two right-angled triangles : 
then find the difference of the segments of the base by Theo- 
rem III. Half this difference being added to half the base, 
gives the greater segment; and, being subtracted from half 
the base, gives the less segment. Then, since the greater 
segment belongs to the right-angled triangle having the greater 
hypothenuse, we have two sides and the right angle of each 
of two right-angled triangles, to find the acute angles. 



EXAMPLES. 



1. The sides of a plane triangle 
being given; viz., BC = 4:0, AC = 34, 
and AB = 25: required the angles. 




SEC. in.] PLANE TBIGONOMETKT. 55 



GEOMETEICALLY. 



With the three given lines as sides, construct a triangle 
as in Prob. IX. Then measure the angles of the triangk- 
eiiher with the protractor or scale of chords. 



TEIGOXOMETEICALLT. 



BC : AC -{- AB :: AC - AB : CD - BD. 

That is, 40 : 59 : : 9 : ^' ^ =13.275. 

40 -f 13.2:5 
Then, ^ = 26.63:5 = CD, 

40-13.2:5 
And, -^ = 13.3625 = BD. 



In the triangle DAC, to find the angle DAC. 
AC \ DC w sin D : sin DAC. 

Applying logarithms, ^e have, 

(a. c.) log .IC (34) 8.468521 

log i)C (26.63:5) 1.425493 

log sin D (90') 10.000000 

lo^ sin DAC 51=^ 34' 40'' . . 9.894014 



In the triangle BAD, to find the angle BAD. 

AB : BD :: sin D : sin BAD. 

Applying logarithms, we have, 

(a, c.) log AB (25) 8.602060 

log BD (13.3625) 1.125887 

log sin D (90") 10.000000 

log sin BAD 32' IS' 35" . . . 9.:2:947 



56 ELEMENTS OF SURVEYING. [BOOK I. 

Hence, 90° - i)v4C = 90° - 51° 34' 40" = 38° 25' 20" = C, 
and, 90° - BAD = 90° - 32° 18' 35" = 57° 41' 25" = B, 
and, BAD + DAC = 51° 34' 40" + 32° 18' 35" = 
= 83° 53' 15" = A. 

2. In a triangle, of whicli the sides are 4, 5, and 6, what 
are the angles ? 

Ans. 41° 24' 35"; 55° 46' 16"; and 82° 49' 09". 

SOLUTION OF EIGHT-AKGLED TRIANGLES. 

73. The unknown parts of a right-angled triangle may be 
found by either of the four last cases; or, if two of the sides 
are giyen, by means of the property that the square of the 
hypothenuse is equal to the sum of the squares of the two other 
sides. Or, the parts may be found by Theorems IV. and V. 

EXAMPLES. 

1. In a right-angled triangle JBA G, 
there are given the hypothenuse BC— 
250, and the base AC = 240 : required 
the other parts. 



C 




To find the angle B. 
By Theorem I., we haye, 

a : h : : sin ^ : sin ^. 
Applying logarithms, we haye, 

(a. c.) log a (250) 7.602060 

log I (240) 2.380211 

log sin A (90°) 10.000000 

log sin B 73° 44' 23" .... 9.982271 
But, (7 = 90° - J? == 90° - 73*= 44' 23" = 16° 15' 37". 



SEC. in.] PLANE TPJGONOMETRY. 67 

To find side AB. 

We have from Theorem IV., 

H : tun C :: d : c. 

Applying logarithms, we have, 

(a. c.) log i2 (90°) 0.000000 

log tan C (16° 15' 37'') . . . 9.464889 
log b (240) 2.380211 

lo^ c 70.0003 1.845100 



2. In a right-angled triangle JBAC, there are given, 
.4C7=384, and ^ = 53° 08'; 
required the remaining parts. 

Ans, AB = 287.96 ; BO = 479.979; C = 36° 52'. 



BOOK II. 

PLANE SURYEYIKG. 

SECTION I. 
MEASUREMENT OF LINES AND ANGLES. 

1. Surveying, in its most extensive signification, com- 
prises all the operations necessary for finding: 

1st. The area or contents of any portion of the surface 
of the earth; 

2d. The lengths and directions of the bounding lines; 
and, 

3d. For making, on paper, an accurate delineation, both 
of the surface and boundaries; which delineation is called a 
Map. 

2. Plane Suevet is that branch in which the curvature 
of the earth is neglected; as it may be when the survey is 
limited to small portions of the surface. 

3. Geodesic Surveying is when the curvature of the 
earth is taken into account, as it must be in all extensive 

surveys. 

4. A Horizontal Plane, is a plane parallel to the water- 
level. If the plane passes through a point on the surface of 
the ^arth, it is tangent to the surface, and also perpendicular 
to the radius passing through the point of contact. 




SEC. I.]' LI^'ES AND ANGLES. 59 

5. A Horizontal Li^'e, is a plane parallel to the water- 
level, or parallel to a horizontal plane. 

6. A Yeetical Plaxe, is a plane pei-pendicular to a hori- 
zontal plane. 

7. A Vertical Lixe, is a line pei'pendicnlar to a hori- 
zontal plane. 

8. Oblique Lixes, are those which are inclined to a hori- 
zontal plane. 

Thns, AB and DC are hori- 
zontal lines; BC and AB are 
yertical lines; and AC and BD 
are oblique lines. 

9. The Horizontal Distance between two points, is the 
horizontal line intercepted between the two yertical lines 
passing through those points. Thus, BC or AB, is the hori- 
zontal distance between the two points A and C, or between 
the points B and D. 

10. A Horizoxtal Angle, is one, whose sides are hori- 
zontal: its plane is also horizontal. A horizontal angle is 
always equal to the angle included hetween hco vertical ^planes 
2)assing through the angular point and the tico objects which 

■ subtend the angle. 

li. A A'ertical Axgle, is one, the plane of whose sides 
is vertical. 

12. Ax Axgle of Eleyatiox, is a vertical angle having 
one of its sides horizontal, and the inclined side above the 
horizontal side. Thus, in the last figure, BAC is the angle 
of elevation from A to C. 

13. An Angle of Depression, is a vertical angle having 
one of its sides horizontal, and the inclined side under the 



60 ELEMENTS OF SURVEYING. " [BOOK H. 

horizontal side. Thus, DC A is the angle of depression from 
C io A, 

14. Ax Oblique An-gle, is one, the plane of whose sides 
is oblique to a horizontal plane. 

15. All lines, which can be the object of measurement, 
must belong to one of the classes aboye named, viz.: 

1st. Horizontal lines; 2d. Vertical lines; 3d. Oblique lines. 

16. All angles may also be divided into three classeSj 
viz. : 

1st. Horizontal angles; whose sides are horizontal. 
2d. Vertical angles; which include angles of elevation and 
angles of depression; and, 

3d. Oblique angles, or those included by oblique lines. 

Measueemext of Lin"es and Akgles. 

17. It has been shown (Bk. L, Art. 45), that at least one 
side and two of the other parts of a plane triangle must be 
giyen, or known, before the remaining parts can be found, by 
calculation. 

When, therefore, distances are to be found, by trigonometrical 
calculations, two preliminary steps are necessary : 

1st. To measure certain lines on the ground; and, 

2d. To measure, the necessary angles. 

Measurementt oe Distan"ces. 

18. Any tape, rod, or chain, divided into equal parts, may 
be used as a measure; and this is called the unit of measure. 
The unit of measure may be a foot, a yard, a rod, or any other 
ascertained distance. 

The measure in general use, is a chain of four rods or 
sixty-six feet in length; it is called Gunter's chain, from the 
name of the inventor. This chain is composed of 100 links. 



SEC. I.] MEASUKEMENT OF DISTANCES. 61 

Every tentli link, from either end, is marked by a small attached 
brass plate, which is notched, to designate its number from 
the end. The division of the chain, into 100 equal parts, is 
very convenient, since the divisions, or links, are decimals of 
the whole chain, and in the calculations are treated as such. 

TABLE. 

1 chain = 4 rods = 66 feet = 792 inches = 100 links. 
1 link is equal to 7.92 inches. 
80 chains = 320 rods = 1 mile. 
40 chains = ^ mile. 
20 chains = i mile. 

19. Besides the chain, there are needed for measuring, ten 
marking-pins, which should be of iron, each about ten inches 
in length and an eighth of an inch in thickness. These pins 
should be strung upon an iron ring, and this ring should be 
attached to a belt, to be passed over the right shoulder, sus- 
pending the pins at the left side. 

To measure a horizontal line. 

20. The point where the measurement is to begin is usually 
located by a staff or stake temporarily placed for the purpose ; 
or by some one of the many permanent marks by which the 
angles in a boundary are fixed. 

The other extremity of the line must be provided with a 
staff or flag which can be easily seen. 

The fore-chain man, with the pins, and one handle of the 
chain in his right, starts off on the line, drawing out the 
chain to its full length. Both chainmen now examine it care- 
fully, to see if there are any "kinks" at the junction of the 
links. Having adjusted the chain for use, the fore-chainman 
resumes his place, to be directed by the hind-chainman, so 
that the measurement shall be made exactly along the estab- 



62 



ELEMENTS OF SURVEYING. 



[book n. 




lished line. To facnitu-te this, and to insure the correct align- 
ment of the pin, at its proper distance, the chain and one 
pin should be held firmly in the 
right hand, as represented in the 
figure. While the pin is being 
aligned, it should be held by the 
fore-chainman as far from the body 
as possible, so that the yiew of the 
flag be left unobstructed. To ac- 
complish this, and at the same time 
draw the chain to the proper degree 
of tension, the right arm should be 
braced against the inside of the 
right knee. 

The hind-chainman directs by the simple orders '' right" or 
" left," according as the pin, held as described, is to be carried 
to the right or left to bring it into line with the flag. When 
the pin is truly in line, the chain at the 
same time being drawn straight, the order 
"down" is given, when the fore-chain- 
man bringing his left hand to bear on 
the top of the pin, forces it vertically 
into the ground, and resumes his course 
to the length of another chain. 

After one or two chains have been 
measured, on any line, the fore-chainman 
can, by glancing back to the station just 

left, place the pin nearly in the right position : the exact 
aligning should be left, however, to the hind-chainman. 

When the distance is more than ten chains, the pins, when 
exhausted, should be returned to the fore-chainman — the dis- 
tance noted — and the chaining recommenced at the place of 
the tenth pin. 




SEC. I.] 



MEASUREMENT OF DISTANCES. 



63 



All distances should be measured liorizontuily : Hence, 
when the ground slopes, one end of the chain must be ele- 
vated. Each chainman should be provided with a small plumb- 
line, so that the elevated end of the chain may be held directly 
over the proper point. 

When the raised end of the chain is only two, or even 
three feet above the ground, it will suffice, in many cases, to 
use a marking-pin, held lightly by the point, between the thumb 
and finger, instead of a plumb-line. When the chaining is on 
a steep inclination, other precautions should be observed. 




Suppose the chaining to be w^j Mil. The fore-chainman 
draws the chain out to its full length, as in any other case, 
and then returns to within such a distance of the hind- 
chainman, that when the chain is drawn out to that length 
horizontally, it shall not be too high to be held conveniently. 

The hind-chainman holds his end of the chain carefully 
over the point or station, by means of the plumb-line, while 
he directs the fore-chainman in the usual manner. 



64 



ELEMENTS OF SURVEYING. 



[book n. 



The point fixed in this manner, by the fore-chainman, must 
not be marked by a marking-pin, but by a small peg or nail. 
At the order, "Down," the fore-chainman does not go forward 
in the usual manner, but waits until the hind-chainman comes 
up and takes the chain by the precise point held, the moment 
before, to the ground. 

■ This point is now held above the peg by the hind-chain- 
man, who uses the plumb, as before, and aligns the fore-chain- 
man, who has taken hold of the chain a few links farther on, 
and is holding it to the ground. These short distances are 
not recorded. 

In chaining down-hill, the method is essentially the same. 
The fore-chainman uses the plumb, and determines by it where 
the peg is to be placed. 

At the end of a course, the part of a chain is measured by 
drawing the chain only to the flag^ where it is held by the fore- 
chainman, until the hind-chainman comes forward to the last 
pin, and counts the links. 

In measuring up the hill from 
A to 0, or down the hill from 
C to A, we measure the horizontal 
distances a t, c d, and / C, and 
their sum is the liorizontal dis- 
tance between A and C. 

Two staves are often used w^th the chain, in the measure- 
ment of lines. Each of these should be about six feet in 
length, and have a spike in the lower end to aid in holding 
it firmly, and a horizontal strip of iron to prevent the chain 
from slipping ofi": each stalf is to be passed through the ring 
at the end of the chain. 




SEC. I.] MEASUEEMEXT OF DISTANCES. 65 

Sta>'"dard. 

21. As the length of the chain may vary, from heat or 
cold, or become changed from other causes, it should be com- 
pared from time to time, with a standard, kept for the purpose. 

To facilitate this comparison, let two stakes be driven in 
the ground, distant from each other one chain, and let nails be 
driven in the heads of the stakes to mark the exact length of 
the standard. 

Marks made upon the coping of a wall will answer the 
same purpose. If it is found that any line has been measured 
with a chain, either too short or too long, the measured dis- 
tance may be corrected by the following proportion: 

As the length of the standard 

the length of the chain 

the measured distance 

the true distance. 

For the correction of areas we have this proportion:. 

As the square of the length of Aie standard 
the square of the length of the chain, 
the area found 
the true area. 

Measurement op A^tgles. 

22. "We come next to the measurement of ^ngles,^. and" for 
this purpose, several instruments are used. T^e one, however, 
which affords the most accurate results, and /which indeed can 
alone be relied on for nice or extended operations, is called a 
Theodolite. This instrument, only, will be described at present; 
others will be subsequently explained. 

5 



66 ELEMENTS OF SURVEYING. [BOOK II. 

The Theodolite. 

23. PI. 1. — The theodolite is an instrument used to measure 
horizontal and vertical angles. It is usually placed on a tripod 
ABC, which enters, by means of a screw, the lower horizontal 
plate DEy and becomes firmly attached to the body of the 
instrument. Through the horizontal plate DE, four small 
hollow cylinders are inserted, which receive four screws with 
milled heads, that w^ork against a second horizontal plate, FG. 
The upper side of the plate DE terminates in a curved sur- 
face, which encloses a ball, that is nearly a semi-sphere, with 
the plane of its base horizontal. This ball, which is hollow, 
is firmly connected with the smaller base of a hollow conic 
frustum, that passes through the curved part of the plate DE, 
and screws firmly into the curved part of the second horizontal 
plate FG. 

A hollow conic spindle passes through the middle of the 
ball, and the hollow frustum with which it is connected. To 
this spindle, a third horizontal and circular plate HI, called 
tlie limb of the instrument, is permanently attached. Within 
this spindle, and concentric with it, there is a second spindle, 
called the inner, or solid spindle. To this latter, is united 
a thin circular plate, called the vernier plate, which rests on 
the limb of the instrument, and supports the upper frame-work. 
The two spindles terminate at the base of the spherical ball, 
where a small screw enters the inner one, and presses a w^asher 
against the other, and the base of the ball. On the upper 
surface of the plate FG, rests a clamp which goes round the 
outer spindle, and which, being compressed by the clamp-screw 
K, is made fast to it. This clamp is thus connected with the 
plate FG. A small cylinder a, is fastened to the j^late FG : 
through this cylinder a thumb-screw L passes, and works into 
a small cylinder h, connected with the clamp. The cylinders 



SEC. I.] OF THE THEODOUTE. 67 

h jind «, admit of a motion round their axes, so that the screw 
L may work through them freely. 

Directly above the clamp, is the lower telescope MN. This 
telescope is connected with a hollow cylinder, which is worked 
freely round the outer spindle, by the thumb-screw P having 
a pinion working into a concealed cog-wheel, that is perma- 
nently fastened to the limb of the instrument. By means of a 
clamp-screw Q, the telescope is made fast to the limb, when it 
will have a common motion with the limb and outer spindle. 

The circular edge of the limb is chamfered, and is generally 
made of silver, and on this circle the graduation for horizontal 
angles is made. In the instrument described, the circle is 
divided into degrees and half-degrees; the degrees are numbered 
from to 360. 

On the circular edge of the vernier plate, is a small plate 
of silver, called a vernier ; this plate is divided into 30 equal 
parts, and numbered from the line marked to the left. Two 
levels, at right angles to each other, are attached to the vernier 
plate by small adjusting screws; one of the levels is seen in the 
figure. 

The vernier plate turns freely around with the inner spindle. 
It is made fast to the limb of the instrument by the clamp- 
screw S; after which the smaller motions are made by the 
tangent-screw T. There is a compass on the vernier plate, that 
is concentric with it, the uses of which will be explained under 
the head. Compass. 

The frame-work which supports the horizontal axis of the 
vertical semicircle UV and the upper telescope, with its attached 
level, rests on the vernier plate, to which it is made fast by 
three adjusting screws, placed at the angular points of an 
equilateral triangle. The vertical semicircle UV, is called the 
vertical limh ; its motions are governed by the thumb-screw Z, 
which has a pinion that works with the teeth of the vertical 



68 ELEMENTS OF SURVEYING. [BOOK n. 

limb. On the face of the vertical limb, opposite the thumb- 
screw Z, the limb is divided into degrees and half-degrees: 
the degrees are numbered both ways from the line marked 0. 
There is a small plate resting against the graduated face of the 
vertical limb, called the vernier; it is divided into 30 equal 
parts, and the middle line is designated by 0. 

On the other face of the vertical limb, are two ranges of 
divisions, commencing at the point, and extending each 
way 45°. The one shows the vertical distance of any object to 
which the upper telescope may be directed, above or below the 
place of the instrument, in 100th parts of the horizontal dis- 
tance: the other, the difference between the hypothenusal and 
base lines — the hypothenuse being supposed to be divided into 
one hundred equal parts: therefore, by mere inspection, wo can 
ascertain the number of links, which must be subtracted from 
every chain of an oblique line, to reduce it to a true horizontal 
distance. 

The supports of the upper telescope are called the wyes, 
and designated ys. Two loops, turning on hinges, pass over 
the telescope, and are made fast by the pins c and d; these 
loops confine the telescope in the Y^s. By withdrawing the 
pins, and turning the loops on their hinges, the telescope may 
be removed for the purpose of being reversed in position; and 
in both situations, the telescope can be revolved in the Y^s 
about its axis. 

In the telescopes attached to the theodolite, are two prin- 
cipal lenses, one at each end. The one at the end where the 
eye is placed, is called the eye-glass, the other the object-glass. 

In order that the axis of the telescope may be directed to 
an object with precision, two spider's lines, or small hairs, are 
iixed at right angles to each other, and placed within the 
barrel of the telescope, and at the focus of the eye-glass. The 
vertical hair is moved by two small horizontal screws, one of 



SEC. I.] OF THE THEODOLITE. 69 

which, /, is seen in the figure ; and the horizontal hair, by two 
yertical screws, g and li. 

Adjustments of the Theodolite. 

24. Before using the instrument, it must be adjusted ; that 
is, the parts must be brought to their proper relative positions. 
There are four principal adjustments. 

FiKST ADJUSTMENT. — To fix tlw intersection of tlie sjiidefs 
lines in tlie axis of tlie telescope, luliicli is called tlie line of 
collimation. 

Having screwed the tripod to the instrument, extend the 
legs, and place them firmly. Then loosen the clamp-screw .S*, 
of the vernier plate, and direct the telescope to a small, well- 
defined, and distant object. By means of a small pin i, on the 
under side of the telescope, slide the eye-glass till the spiders 
lines are distinctly seen; then with the thumb-screw X, which 
forces out and draws in the object-glass, adjust this glass to its 
proper focus, when the object, as well as the spider's lines, will 
be distinctly seen : after which, by the tangent-screw T and the 
thumb-screw Z, bring the intersection of the sj^iders lines 
exactly upon a well-defined point of the object. 

Having done this, revolve the telescope in the Y^s half 
round, when the attached level mn will come to the u^^per side. 
See if, in this position, the horizontal hair appears above or 
below the point; and in either case, loosen one, and tighten 
the other, of the two screws that work the horizontal hair, 
till the horizontal hair has been carried over half the space 
between its last position and the observed point. Carry the 
telescope back to its place ; direct again the intersection of the 
spiders lines to the point, and repeat the operation till the 
horizontal hair neither ascends nor descends, while the telescope 



70 ELEMENTS OF SUKYEYING. [BOOK H. 

is revolved. A similar process ^ill arrange the vertical hair, 
and the line of collimation is then adjusted. 

Secoxd ADJUSTMENT. — To mctlce the axis of the attached level 
of the ui^per telescope, ^parallel to the line of collimation. 

Turn the vernier plate, till the telescope comes directly over 
two of the levelling screws, between the plates DE and FG. 
Turn these screws contrary ways, keeping them firm against 
the plate FG, till the bubble of the level mn stands at the 
middle of the tube. Then, open the loops, and reverse the 
telescope. If the bubble still stands in the middle of the tube, 
the axis of the tube is horizontal: but if not, it is inclined, the 
bubble being at the elevated end. In that case, by means of 
the small vertical screws m and n, at the ends of the level, 
raise the depressed end, or depress the elevated one, half the 
inclination : and then, with the levellins: screws, brinc( the level 
into a horizontal position. Ee verse the telescope in the Y's, 
and make the same correction again ; and so on, until the 
bubble stands In the middle of the tube, in both positions of 
the telescope : the axis of the level is then horizontal. Let the 
telescope be now revolved in the Y's. If the bubble continue 
in -the middle of the tube, the axis of the level is not only 
horizontal, but also parallel to the line of collimation. If, hov\-- 
ever, the bubble recede from its centre, the axis of the level is 
inclined to the line of collimation, and must be made parallel 
to it by means of two small antagonistic screws (one of which 
is seen at js), which work horizontally. By loosening one of 
them, and tightening the other, the level is soon brought 
parallel to the line of collimation, and then, if the telescope 
be revolved in the Y's, the bubble will continue in the middle 
of the tube. 

It is difficult to make the first part of this adjustment, 
while the axis of the level is considerablv inclined to the line 



SEC. I.] OF THE THEODOLITE. 71 

of collimation ; for, if the level were truly horizontal in one 
position of the telescope, when the telescope is reversed, the 
bubble would not stand in the middle of the tube, except in 
one position of the level. This suggests the necessity of making 
the first part of the adjustment with tolerable accuracy; then, 
liaving made the second with care, let the first be re-examined, 
and proceed thus till the adjustment is completed. 

Third adjustment. — To mcike the axes of tlie levels, on the 
liml), ijeryendicular to the axis of the instrument. 

This adjustment is effected, partly by the levelling screws, 
and partly by the thumb-screw Z. Turn the vernier plate, 
until the upper telescope comes directly over two of the 
levelling screws, then turn the screws contrary ways, till the 
upper telescope is horizontal; after which, turn the vernier 
plate 180°, and if the bubble of the level remains in the middle 
of the tube, one line of the limb is horizontal. But if the 
bubble recedes from the centre of the level, raise the lower, or 
depress the upper end, one-half, by the levelling screws, the 
other by the thumb-screw Z, till it is brought into a horizontal 
position. Turn the vernier plate again 180°, and if the level 
be not then horizontal, make it so, by dividing the error as 
before, and repeat the operation until the line of the limb is 
truly horizontal. Then turn the vernier plate 90°, and level 
as before. The limb ought now to be truly horizontal; but, 
lest the first horizontal line may have been changed, in ob- 
taining the second, it is well to bring the telescope and level, 
two or three times over the levelling screws, until an entire 
revolution can be made without displacing the bubble from 
the middle of the tube. As this can only take place when the 
level revolves around a vertical line, it follows that the limb 
will then be horizontal, and the axis of the instrument vertical. 
Then, by means of the small screws at the ends of the levels, 



72 ELEMENTS OF SURVEYING. [BOOK II. 

bring the bubbles to the centres, and the axes of the levels 
will be perpendicular to the axis of the instrument. 

Fourth adjustment. — To make the axis of tlie vertical limb 
perpendicular to the axis of the instrument. 

Bring the intersection of the spider's lines of the upper 
telescope upon a plumb-line, or any well-defined vertical object, 
and move the telescope with the thumb-screw Z : if the inter- 
section of the spider's lines continues on the vertical line, the 
axis is horizontal. 

Or, the adjustment may be efiected thus: Direct the inter- 
section of the spider's lines to a well-defined point that is 
considerably elevated: then turn the vertical limb, until the 
axis of the telescope rests on some other well-defined point, 
upon or near the ground: reverse the telescope, and turn the 
vernier plate 180° ; then, if in elevating and depressing the tele- 
scope, the line of collimation passes through the two points 
before noted, the axis is horizontal. If it be found, by either of 
the above methods, that the axis is not horizontal, it must 
be made so by the screws which fasten the frame-work to 
the vernier plate. 

There are two important lines of the theodolite, the positions 
of which are determined with great care by the maker, and 
fixed permanently. First, the axis of the instrument is placed 
exactly at right angles Avith the limb and vernier plate ; and 
unless it have this position, the vernier plate will not revolve 
at right angles to the axis, as explained in the third adjust- 
ment. 

Secondly, the line of collimation of the upper telescope is 
fixed at right angles to the horizontal axis of the vertical limb. 
We can ascertain whether these last lines are truly at right 
angles, by directing the intersection of the spider's lines to a 
well-defined point ; then removing the caps which confine the 



SEC. I.] VERNIERS. 73 

horizontal axis in its supports, and reversing the axis : if the 
intersection of the spider's lines can be made to cover exactly 
the same point, without moving the vernier plate, the line of 
collimation is at right angles to the axis. 

If the theodolite be so constructed that either of the Y's 
admits of being moved laterally, so as to vary the angle between 
the horizontal axis and the line of collimation, these lines may 
be adjusted at right angles to each other, if they have not 
been so placed by the maker. 

The lower telescope, being used merely as a guard, requires 
no adjustment, although it is better to make the axis, about 
which its vertical motions are performed, horizontal, or per- 
pendicular to the axis of the instrument ; and this is easily 
effected by means of the two small screws h and /, which 
work into the slide A', that is connected with the horizontal 
axis. 

Having explained the methods of properly adjusting the 
theodolite, we Avill now explain the particular uses of its 
several parts in the measurement of angles. 

Verniers. 

25. Before explaining the vernier, as applied to the the- 
odolite, we shall discuss the general theory of verniers. 

A Vernier is a contrivance for measuring smaller arcs than 
those into which the limb of an instrument is divided. 
,' It is a graduated scale, so arranged, as to cover an exact 
number of equal spaces on the primary scale or Umi, to v/hich 
it is applied. It is divided into a number of equal parts, 
greater by one than the number of equal spaces which it 
covers on the limb. 

The vernier may be applied to any limb or scale of equal 
parts. The modes of its application are extremely various ; 



74 ELEMENTS OF SURVEYING. [BOOK II. 

the principle, however, is the same in all, and may be illus- 
trated by a simple diagram. 

S £> iO 1J J2 13 I'h iS 16 17 IS 19 

a\ \ j \ I \ \ \b 



i j 














n ! 1 i 1 1 1 1 1 1 


JJ 



Let yl^ be any Ihnb or scale of equal parts, one of which 
let us suppose equal to d. Let CD be a vernier, equal in 
length, say to nine of these parts, and itself divided into ten 
equal spaces, each one of which is then equal to nine-tenths 
of l. The difference between a space on the limb and a space 
on the vernier, is therefore equal to one-tenth of 1), or -^^1). 
This is the least space that can be measured b}' means of the 
vernier, and is called the least count ; hence. 



The least count of a vernier is equal to one of the 
divisions of the limh divided ly the numher of spaces on the 
vernier. 

Eeadi:n'GS. 

26. The true reading of an instrument, for any position ol 
the vernier, expresses the distance from the point where the 
graduation on the limb begins, marked 0, to the point of 
the vernier. In the diagram, that distance is expressed by 
nine units of the limb, or 9. 

If, now, the vernier be moved till the division 1 coincides 
with, the division 10 of the limb, the point will have ad- 
vanced along the limb a distance equal to -^-qI), and the reading 
will become 9 + -^^h. If w^e again move the vernier till the 
division 2 coincides with the division 11 of the limb, the 
point will have advanced an additional distance, equal to 
yV ^j and the reading becomes ^ + -^^1 ; when 3 coincides with 
division 12, the reading will become 9 -f y%&, and so on, till 



SEC. I.] ' MEASUREMENT OF ANGLES. 75 

finally, when the point 10 coincides with 19 of the limb, the 
distance 9 will have been increased by-ff &, and will become 10, 
as it should, since, in that case, the point will have been 
moved a whole space, and will coincide with the division 10 
of the limb. Hence, the following rule for reading an instru- 
ment which has a vernier: 

Read the Imd in ihe direction of the graduation iip to the 
division tine next preceding the j^oi/it of the vernier ; this is 
called the reading on the limb. Look along the vernier till a 
line is found to coincide tvith a line of the Umh : multiply the 
number of this first line by the least count of the vernier: this 
is the reading on the vernier: the sum of these two readings is 
the reading of the instrument. 

In the theodolite described, the limb is divided into half- 
degrees, and 30 spaces on the vernier cover 29 spaces on the 
limb. Hence, the least count of this instrument is 3V of a 
half-degi*ee, or 1'. Fig. 2, Plate 1, exhibits the vernier of the 
horizontal limb, and Fig. 3, the vernier of the vertical limb. 

To Measure a Hoeizoxtal Axgle with the Theodolite. 

27. Place the axis of the instrument directly over the point 
at which the angle is to be measured. This is effected by 
means of a plumb, suspended from the centre of the plate 
which forms the uj^per end of the tripod. 

Having made the limb truly level, place the of the vernier 
at 0, or 360° of the limb, and fasten the clamp-screw S of the 
vernier plate. Then, facing in the direction between the lines 
which subtend the angle to be measured, turn the limb with 
the outer spindle, until the telescope points to the object on the 
left, very nearly. Clamp the hmb T\ith the clamp-screw K, and 
by means of the tangent-screws L and Z, bring the intersection 
of the spiders lines to coincide exactly with the object. 



76 ELEMENTS OF SURVEYING. [BOOK II. 

Having loosened the clamp-screw ft of the lower telescope 
MN, direct it with the thumb-screw P to the same object at 
which the npper telescope is directed; then tighten the clamp- 
screw Q. This being done, loosen the clamp-screw 8 of the 
vernier plate, and direct the telescope to the other object : the 
arc passed over by the point of the vernier, is the measure 
of the angle sought. 

The lower telescope having been made fast to the limb, will 
indicate any change of the position of the limb, should any 
have taken place; and, as the accuracy of the measurements 
depends on the fixedness of the limb, the lower telescope ought 
to be often examined, and, if its position has been altered, the 
limb must be brought back to its place by the tangent-screw L. 

Note. — It is not necessary to place the point of the vernier 
at the point of the limb, previously to commencing the 
measurement of the angle, but convenient merely; for, what- 
ever be the position of this point on the limb, it is evident that 
the arc which it passes over is the true measure of the hori- 
zontal angle. If, therefore, its place be carefully noted for the 
first direction, and also for the second, the difierence of these 
two readings will be the true angle, unless the point of the 
vernier shall have passed the point of the limb, in which 
case the greater reading must be subtracted from 360°, and the 
remainder added to the less. 

Measurement oe Vertical Angles. 

28. We shall first explain the method of determining the 
index error. Having levelled the horizontal limb, direct the 
telescope to some distinctly marked object, as the top of a 
chimney, and read the instrument. Reverse the telescope in 
the Y's, and turn the vernier plate 180°, and having directed 



SEC. I.] MEASUREMENT OF VERTICAL ANGLES. 77 

the telescope to the same object, again, read the instrument. 
If the two readings are the same, the limb is adjusted; that is, 
the of the limb coincides with the of its vernier, when the 
axis of the telescope is parallel to the horizontal limb. 

TVhen the reading, found with the eye end of the telescope 
nearest the yernier, is greater than that obtained in the reversed 
position, the true elevation of the object, which is equal to a 
mean of the readings, may be obtained by subtracting half the 
difference from the first reading. If the first reading is less 
than the second, the half difference must be added to the 
first. Hence, 

To find, the index error, take tlie reading of tlie limb iclien 
tlie telescope is directed to a fixed object, first with the eye end 
of the telescope nearest the vernier, and then with the telescope 
and vernier plate both reversed. Take half the difference of these 
readings, and affect it vAtli a minus sign if the first is the 
greater, or a plus sign if the second is the greater; this is equal 
to the index error. 

Let the operation be repeated several times, using different 
objects, and a mean of the errors will be more correct than the 
result of a single observation. 

29. Having determined the index error, let the axis of the 
telescope be directed to any point either above or below the 
plane of the limb, and read the arc indicated by the of the 
vernier. To the arc so read, apply the proper correction, if 
any, and the result will be the true angle of elevation or 
depression. 

The angle of elevation may be more coiTectly found by 
taking the elevation of the object, and repeating the observation 
with the telescope and vernier plate reversed, and then taking 
a mean of the readings for the angle required. 



78 ELEMENTS OF SURYEYING. [BOOK II. 

Measurements with the Tape or Chaix o:n^ly. 

30. It often happens that instruments for the measurement 
of angles cannot be easily obtained ; we must then rely entirely 
on the tape or chain. 

AVe now propose to explain tlie best methods of determining 
distances, without the aid of instruments for the measurement 
of horizontal or vertical angles. 

I. To trace, on the ground, the direction of a right line, that shall 
be perpendicular at a given point, to a given right line. 

FIRST METHOD. 

31. Let BC he the given right line, and A the given point. 
Measure from A, on the line BC, two equal distances AB, AC, 
one on each side of the point A. Take a 
portion of the chain or tape, greater than '^^ 
AB, and place one extremity at B, and 
with the other, trace the arc of a circle on 
the ground. Then remove the end which 

was at B to C, and trace a second arc intersecting the former 
at B. The straight line, drawn through D and A, will be per- 
pendicular to BC at A, 

SECOND METHOD. 

32. Having made AB = AC, take any portion of the tape 
or chain, considerably greater than the 
distance between B and C. Mark the 
middle point of it, and fasten its two 
extremities, the one at B and the other 
at C. Then, taking the chain by the ^ 
middle point, stretch it tightly on either side of BC, and place 
a staff at I) or E : DAE will be the perpendicular required. 




SEC. I.] MEASUREMENTS WITH THE CHAIN. 79 



THIRD METHOD. 



C 



33. Let AB be tlie given line, and C the point at which 
the perpendicular is to be drawn. From ^ 

the point C, measure a distance CA equal ^ 

to 8. With G as a centre, and a radius 

equal to 6, describe an arc on either side 

Qi AB : then, with ^ as a centre, and a 

radius equal to 10, describe a second arc K 

intersecting the one before described, at E: then draw the line 

EC, and it will be perpendicular to AB at C. 

Note. — Any three lines, having the ratio of 6, 8, and 10, 
form a right-angled triangle, of which the side corresponding 
to 10 is the hypothenuse. 

FOURTH METHOD. 

34. Let AD be the given right 
line, and D the point at which the 
perpendicular is to be drawn. Take 
any distance, on the tape or chain, 
and place one extremity at i), and 

fasten the other at some point, as E, "* 

between the two lines which are to form the right angle. Place 
a staff at E. Then, having stationed a person at D, remove that 
extremity of the chain and carry it round until it ranges on 
tlie line DA, at A. Place a staff at A : then remove the end 
of the chain at A, and carry it round until it falls on the line 
AE, prolonged, at F. Then place a staff at F ; ADF will be 
a right angle, being an angle in a semicircle. 

Note. — There is a very simple instrument, used exclusively 
in laying off right angles on the ground, which is called 
the 




80 ELEMENTS OF SURVEYING. [BOOK IL 

Sukyeyor's Cross. 

35. This iustriiment consists of two bars, AB and CD, PI. 2, 
Fig. 1, permanently fixed at right angles to each other, and 
firmly attached at E, to a pointed staff, which serves as a 
support. Four sights are screwed firmly to the bars, by means 
of the screAvs a, 1), c, and d. 

As the only use of this instrument is to lay ofi* right angles, 
it is of the first importance that the lines of sight be truly ajt 
right angles. To ascertain if they are so, let the bar ^^ be 
turned until its sights mark some distinct object; then look 
through the other sights, and place a staff on the line which 
they indicate: let the cross be then turned until the sights 
of the bar AB come to this last line: if the other sights are 
directed to the first object, the lines of sight are exactly at 
right angles. 

The sights being at right angles, if one of them be turned 
in the direction of a giyen line, the other will mark the direc- 
tion of a line perpendicular to it, at the point where the in- 
strument is placed. 

n. Prom a given point -without a straight line, to let fall a per- 
pendicular on the line. 

86. Let C be the given point, and AB the given line. 

From Cj measure a line, as CA, ^ 

to any point of the line AB. From ^ 

A, measure on AB any distance as 
AF, and at F erect FE perpendicu- ^ •*' 

lar to AB. 

Haying stationed a person at A, measure along the perpen- 
diculaj: FE until the forward staff is aligned on the line Ad 




C 



SEC. I.] MEASUREMENTS TVITH THE CHAIN. 81 

then measure the distance AE. JSTow, bj similar triangles, we 

have, 

AE '. AF :: AC : AD, 

in whicli all the terms are known except AD, which may, 
therefore, be found. The distance AD being laid off from A, 
the point D, at which the perpendicular CD meets AB, be- 
comes known. If we wish the length of the perpendicular, 
we use the proportion, 

AE : EF :: AC : CD, 

in which all the terms are known, excepting CD: therefore, 
CD is determined. 

III. To determine the horizontal distance from a given point to an 
inaccessible object. 

FIEST METHOD. 

37. Let A be an inaccessible object, and E the point from> 
which the distance is to be measured. 

At E, lay off the right angle AED, | 

and measure in the direction ED, jp 

any conyenient distance to D, and ^-- ,'-'' I 

place a staff at D. Then measure ^r^-''" f 

from E, directly towards the object n ^^--^ • 
A, a distance EB of any conyenient D F ^ 

length, and at B, lay off a line BC perpendicular to EA, 
Measure along the line BC, until a person at D shall range 
the forward staff on the line DA. Xow, DF is known, being 
equal to the difference between the two measured lines DE 
and CB. Hence, by similar triangles, 

DF : FC :: DE : EA, 

in which proportion all the terms are known, except the fourth, 
which is therefore found. 



82 



ELEMENTS OF SURVEYING. 



[book II. 



-^A:- 



r^.. 



SECOND 3IETnOD. 

38. At the point E, lay off BB 
perpendicular to the Ime BA, and 
measure along it any convenient 
distance, as BB. 

At B lay off the right angle f 
EBB, and measure any distance %/ 
in the direction BB. Let a person I) 

it D align a staff on BA, ^'hile a second person at B aligns 
it on BE : the staff will thus be fixed at C. Then measure 
the distance BC. 

The two triangles BCB and CAB being similar, we 

have, 

BC : BB :: CE : EA, 

in which all the terms are known, except the fourth, which is, 
therefore, found. 

THIED METHOD. 

39. Let B be the given point, and A tlie inaccessible object; 
it is required to find i>^. 

Measure any horizontal base-line, 
as BC. Theu, having placed staves 
at B and C, measure any conve- 
nient distances BB and CE, such 
that the points B, B, and A, shall 
be in the same right line, as also, 

the points E, C, and A ; then meas- d / ^.-^^-^ \ s 
ure the diagonal lines BC and BB. o*^ ^^ 

K'ow, in the triangle BBC, the three sides are known, there- 
fore, the angle BCB can be found. In the triangle CBB, the 
tliree sides are also known, therefore the angle CBB can be 
determined. These angles being respectively subtracted from 
180"^, the two angles ACB and ^li? (7 become known; and hence, 




SEC. L] 



MEASUREMENTS. 



83 



ill the triangle ^i^ 6', we have two angles and the included side, 
to fxud the side JBA. 

POURTH METHOD. 

40. Let AC be the distance 
required. Lay off the right angle 
CAB, and measure AB, any con- 
venient distance. At B lay off the 
right angle CBI), and fix the point 
D, carefully, in line with AC. 
Measure AD. Then, 



AD:AB::AB:AC.'.AC = 



AD. 




(Legendre, Bk. IV., Prop. 23.) 

XoTE. — When such problems 
occur in practice, the distance AC 
is usually a portion of a longer line, so that the line CAD is 
well marked by stakes or pins, before AB is measured. 



IV, To prolong a line beyond an obstacle. 

41. Let OA be the line to 
be 'prolonged. Lay off GAB 
= 120°, or CAB = G0°. Meas- 
ure AB, of such length as to 
permit BC to be 'measured 
without meeting the obstruc- 
tion. Make ABC =60°, and 
measure BC, equal to AB. If 
A be not in sight from C, 
make the angle BCF equal to 120'', and resume the survey of 
the line. ^C is equal to AB or BC. 

XoTE. — This method may be employed in the absence of 
any angular instruments, by constructing an equilateral triangle 
with the chain. Holding together the end of the chain with 




84 ELEMENTS OF SURVEYING. [BOOK II. 

tlie 90-link point, let two assistants draw out at the 30, and 
at the 60 point, until the three lines are straight. 

V. To find the altitude of an object, when the distance to the 
vertical line passing through the top of it is known. 

42. Let CD be the altitude required, and AC the known 
distance. 

From A, measure on the 
line A C, any convenient dis- 
tance AB, and place a staff 

vertically at B. Then placing ^ ,---'''[ ^^^^^^^^-^^--^^^ 
the eye at A, sight to the '^^ • B C 

object B, and let the point, at which the line AB cuts the staff 
BE, be marked. Measure the distance BE on tlie staff; then, 

AB : BE :: AC. : CD, 
whence CB becomes known. 

If the line AC cannot be measured, on account of inter- 
vening objects, it may be determined by calculation, as in the 
last problem, and then, having found fhe horizontal distance, 
the vertical line is readily determined, as before. 

Applications to Heights axd Distaxces. 

I. To determine the horizontal distance to a point which is inaccess- 
ible by reason of an intervening river.* 

43. Let C be the point. Measure 
along the bank of the riyer a hori- 
zontal base-line AB, and select the 
stations A and B, in such a manner 
that each can be seen from the other, 
and the point G from both of them. 
Then measure the horizontal angles 
CAB and CBA, with an instrument adapted to that purpose. 

* Read, definitions, from 3 to 14, pages t9 and S9. 




SEC. I.] HEIGHTS AND DISTANCES. 85 

Let us suppose that we have measured AB = 600 yards; 
CAB = A = 5r 35", and CBA = B = 64:° 51'. 
Then, C = 180° - (A + B) = 57° 34'. 

To find the distance BC 

sin C : sin A : : AB : BC. 
Applying logarithms, we have, 

(a. c.) log sin G (57° 34') 0.073649 

log sin A (57° 35') 9.926431 

log AB (600) 2.778151 

log BC 600.11 2.778231 

To find the distance AC 

sin C : sm B : : AB : AC, 

and applying logarithms, we have, 

(a. c.) log sin C (57° 34') 0.073649 

log sin B (64° 51') 9.956744 

log AB (600) 2.778151 

log AC 64:3 Ad 2.808544 

n. To determine the altitude of an inaccessible object above a given 
horizontal plane. 

FIEST METHOD. 

44. Suppose D to be an inaccess- x> 

ible object, and BC the horizontal --^"'''I^^ 

plane from which the altitude is to Q^j..i .=^i.Z..^ 

be measured: then, if we suppose D (7 n^ -^ y,^^ 

to be a vertical line, it will represent Nr"*/^''' 

the required distance. ^ 

Measure any horizontal base-line, as BA; and at the ex- 
tremities B and A, measure the horizontal angles CBA and 
CAB. Measure, also, the angle of elevation BBC. 

Then, in the triangle CBA, there will be known, two angles 



86 ELEMENTS OF SURVEYIKG. [BOOK II. 

and the side AB ; the side BG can therefore be found by 
calculation. Having found BC, we shall haye, in the right- 
angled triangle DBC, the base BC and the angle at the base, 
to find the perpendicular DC, which measures the altitude of 
the point D, aboye the horizontal plane BC. 

Let us suppose that we haye found, by measurement, 

BA — 780 yards. 

The horizontal angle CBA = i? = 41° 24', 

the horizontal angle CAB = A = 96° 28', 

and the angle of eleyation DBC = 10° 43'. 

To find, in the triangle BCA, the horizontal distance BC. 
The angle BCA = C = 180° - (^1 + B) = 42° 08'. 
Then, sin C : sin ^ : : AB : BC; 

and applying logarithms, we haye, 

(a. c.) log sin C (42° 08') 0.173369 

log sin A (96° 28') 9.99?228 

log AB (780) 2.892095 

log BC 1155.29 yards . . . 3.062692 

In the right-angled triangle DCB, to find DO. 

We haye, from Theorem IV., 

E : tan DBC : : BC : DC. 
Applying logarithms, we haye, 

(a. c.) log R (90°) 0.000000 

log tan DBC (10° 43') . . . 9.277043 
log BC (1155.29) . . . 3.062692 

loo- DC 218.64 .... 2.339735 



Note 1.— It might, at first, appear, that the solution which 
we haye giyen, requires that the points B and A should be in 



SEC. I.] HEIGHTS AND DISTANCES. 87 

the same liorizontal plane; bat it is entirely independent of 
such a supposition. 

For, the horizontal distance, represented by BA, is the same, 
whether the station A is on the same level with B, above it, 
or below it. The horizontal angles CAB and CBA are also 
the same, so long as the point C is in the vertical line DC. 
Therefore, if the horizontal line throngh A should cut the ver- 
tical linei^C, at any point, as E, above or below C, AB would 
still be the horizontal distance between B and A, and AE, 
would be the horizontal distance between A and C. 

If at A, we measure the angle of elevation at the point D, 
we shall know in the right-angled triangle DAE, the base AE, 
and the angle at the base; from which the perpendicular DE 
can be determined. 

Let us sux)pose that we had measured the angle of elevation 
DAE, and found it equal to 20° 15'. 

First : In the triangle BAG, to find AC, or its equal AE. 
sin C \ sin B :: AB : AC or AE. 
Applying logarithms, we have, 

(a. c.) log sin C (^2° OS') 0.1T33C9 

log sin B (41° 21') 9.820406 

log AB (TSO) 2.892095 

log AE 768.9 2.885870 

In the right-angled triangle DAE, to find DE. 
TTe have, from Theorem IT., 

E : tan A : : AE : DE : hence, 
(a. c.) log E (90°) ..'.... 0.000000 
; log tan A (20° 15") .... 9.566932 
log AE (768.9) 2.885870 

lo^ DE 283.66 2.452802 



88 



ELEMENTS OF SUKVEYIXa. 



[book II. 



Now, since DC is less than DB, 
it follows that the station B is above 
the station A, That is, 

DE - DC = 283.66 - 218.64= 
65.02 = EC, 
which expresses the vertical distance 
that the station B is above the station A 




Note 2. — It should be remembered, that the vertical dis- 
tance which IS obtained by the calculation, is estimated from 
a horizontal line passing through the eye, at the time of ob- 
servation. Hence, the height of the instrument is to be added, 
in order to obtain the true result. 



SECO:NrD METHOD. 

45, When the nature of the ground will admit of it, 
measure a base-line AB, in the direction of the object D. 
Then measure, with the instrument, the angles of elevation 
at A and B. 

Then, since the outward 
angle DBC is equal to the 
sum of the angles A and 
ADB, it follows that, the 
angle ADB is equal to the 

difference of the angles of elevation at A and B. Hence, we 
can find all the parts of the triangle ADB. Having found DB, 
and knowing the angle DBC, we can find the altitude DC. 

This method supposes that the stations A and B are on the 
same horizontal plane ; and therefore it can only be used when 
the line ^^ is nearly horizontal. 

Let us suppose that we have measured the base-line and 
the two angles of elevation, and found, 




SEC. I.] HEIGHTS AND DISTANCES. 89 

AB = 975 yards, A = 15° oG', and DBC = 27° 29'; 
required the altitude DC. 

First: ADB = BBC - A = 27° 29' - 15° 36' = 11° 53'. 

In the triangle ADB, to find BD = c. 

sin D : sin ^ : : AB : DB ; hence, 
(a. c.) log sin D (11° 53') .... 0.686302 
log sin A (15° 36') .... 9.429623 
log AB (975) . 2.989005 ' 

log BD 1273.3 3.104930 

In the triangle DEC, to find DO = b. 
We have, Theorem I.. 

E : sin B :: BD : DC; hence, 

(a. c.) log B (90°) 0.000000 

log sin B (27° 29') .... 9.664163 
log C (1273.3) 3.104930 



log DC 587.61 2.769093 



m. To determine the perpendicular distance of an object below a 
given horizontal plane. 

46. Suppose C to be directly over 
the giyen object, and A the point 
f through which the horizontal plane 
is supposed to pass. 

Measure a horizontal base-line 

AB, and at the stations A and B 
conceive the two horizontal lines 

AC, BC, to be drawn. The oblique lines from A and B, to the 
object, are the hypothenuses of two right-angled triangles, of 
which AC, BC, are the bases. The perpendiculars of these 




90 ELEMENTS OF SUEVEYING. [BOOK H. 

triangles are the distances from the horizontal lines AC, BC, 
to the object. If we turn the triangles about their bases AC, 
BC, until they become horizontal, the object, in the first case, 
will fall at C, and in the second at C". 

Measure the horizontal angles CAB, CBA, and also the 
angles of depression C'AC, C'BC. 

Suppose that we have measured, and found AB = 6T2 yards; 
BAC=n° 29'; ABC =39° 20'; angle of depression C'AC = 
27° 49', and C'BC =19° 10'. 

First: In the triangle ABC, the horizontal angle ACB = 
180° - {A + B) = 180° - 111° 49' = 68° 11'. 

To find the horizontal distance AO 

sin C : sin jS : : AB : AC ; hence, 

(a. c.) log sin C (68° 11') 0.0322T5 

log sin^ (39° 20') 9.801973 ,. 

log AB (672) 2.827369 

log AC 458.79 ...... 2.661617 

To find the horizontal distance EC. 
sin C : sin A :: AB : BC; whence, 

(a. c.) log sin C (68° 11') 0.032275 

log sin A (72° 29') 9.979380 

log AB (672) 2.827369 

lo^ BC 690.28 2.839024 

In the right-angled triangle CAC, to find CC. 
We have, Theorem IV., 

E : tan A :: AC : CC; whence, 

(a. c.) log E (90°) ^ 0.000000 

log tan A (27° 49') 9.722315 

log AC 458.79 2.661617 

los CC 242.06 ..... 2.383932 



SEC. I.] HEIGHTS AND DISTAIJCES. 91 

In the triangle CBC", to find CC" = b. 

We have, Theorem IV., 

E : tun B :: BC : CC"; whence, 

(a. c.) log E (90°) ....... 0.000000 

log tan B (19° 10') .... 9.541061 

log BC (690.28) 2.839024 

log CC" 239.93 2.380085 

Hence, also, CC - CC" = 242.06 - 239.93 = 2.13 yards; 
which is the height of station A aboye station B. 

PEOBLEMS. 

1. Wanting to know the distance between two inaccessible 
objects, which lie in a direct leyel line from the bottom of a 
tower 120 feet in height, the angles of depression are nieasnred 
from tli^MI of the tower, and are found to be, of the nearer 
57°, and of the more remote 25° 30': required the distance 
between the objects. Ans. 173.656 feet. 

2. In order to find the distance be- 
tween two trees, A and B, w^hich could 
not be directly measured because of a 
pool which occupied the intermediate 
space, the distances of a third point C 
from each of them were measured, and 
also the included angle ACB : it was found that, 

CB = 672 yards, 

CA = 588 yards, 

ACB = 55° 40'; 
required the distance AB. Ans. 592.967 yards. 

3. Being on a horizontal plane, and wanting to ascertain 
the height of a tower, standing on the top of an inaccessible 




92 



ELEMENTS OF SURVEYING. 



[book n. 



hill, there were measured, the angle of elevation of the top 
of the hill 40°, and of the top of the tower 51°; then measur- 
ing in a direct line 180 feet farther from the hill, the angle 
of eleyation of the top of the tower was 33° 45': required the 
height of the tower. 



Ans. 83.998. 



4. TTanting to know the hori- 
zontal distance between two inac- 
cessible objects U and W, the fol- 
lowino: measurements were made. 



■':iw 






'AB = 536 yards 




BAW= 40° 16' 


yiz., - 


. WAB = 57° 40' 




ABB = 42° 22' 




BBW= 71° 07'; 


required i 


-he distance BW. 




5. Wanting to know the 
horizontal distance between two 
inaccessible objects A and B, 
and not finding any station 
from which both of them could 
be seen, two points C and B, 
were chosen at a distance from each other, equal to 200 yards ; 
from the former of these points A could be seen, and from the 
latter B, and at each of the points C and B a staff was set up. 
From C a distance CF was measured, not in the direction BC, 
equal to 200 yards, and from B a distance BB equal to 200 
yards, and the following angles taken, 

fAFC = 83° 00', BBB = 54° 30', 
Tiz., iACB= 53° 30', BBC = 156° 25', 
ACF= 54° 31', BBB = 88° 30'. 

Ans. AB = 345.467 yards. 



SEC. I.] HEIGHTS AND DISTANCES. 93 

6. From a station P there can be seen three objects, A, B, 
and C, whose distances from each other are known : yiz., 

AB = 800, AC = 600, and BC = 4:00 yards. 

Now, there are measured the horizontal angles, 

APC = 33° 45', and BPC = 22" 30' : 

it is required to find the three distances, PA, PC, and PB, 




^-. 



GEOMETRICALLY. 

With the three given sides construct 
the triangle AB C. Then, at A lay off the 
angle PAD = 22° 30', and at P the angle 
APP = 33° 45', and note P, the point at 
which the two lines intersect. 

Through the points A, P, and B de- 
scribe the circumference of a circle, and 
through C and P draw the line CPPj 
the point P in which it intersects the circumference, will be 
the position of the station. 

By obserying the equal angles in the figure, the trigono- 
metrical solution is not difficult. "We find, 

[ PA = 710.193 yards. 
Ans. <PC = 1042.522 " 
( PP = 934.291 " 

INToTE. — This problem is much used in maritime surveying, 
for tiie purpose of locating buoys and sounding-boats. The 
trigonometrical solution is somewhat tedious, but the geomet- 
rical solution is very easy, as shown above. 



94 ELEMENTS OF SURVEYING. [BOOK H. 

SECTION II. 

AREA OR CONTENTS OF GROUND. 

47. We come next to the determination of the area or 
superficial contents of ground. 

The surface of ground being, in general, broken and uneven, 
it is impossible, without great trouble and expense, to ascertain 
its exact area or contents. To avoid this inconvenience, it has 
been agreed to refer every surface to a horizontal plane : that is, 
to regard all its bounding lines as horizontal, and its area as 
measured by that portion of the horizontal plane which the 
boundary lines enclose. 

For example, if A BCD were a 
piece of ground, having an uneven 
surface, we should refer the whole 




to a horizontal plane, and take for ii^^'^S^S^^^^ 
the measure of the area that part ''"^^% 0^^^^^^/-'"^^' 
of the plane which is included be- "^^^S'A^ 

tween the bounding horizontal lines AB, BC, CD, DA. 

In estimating land in this manner, the sum of the areas of 
all the parts, into which a tract may be divided, is equal to the 
area, estimating it as an entire piece: but this would not be 
the case if the areas of the parts had reference to the actual 
surface, and the area of the whole were calculated from its 
bounding lines. 

48. The unit of measure of any quantity is a quantity of 
the same kind, regarded as a standard. For lines, the unit is a 
right line of a known length, as 1 foot, 1 link, 1 chain, or any 
other fixed distance. 

It has been already observed (Bk. II., Kri. 18), that Gunter's 
chain of four rods or 66 feet in lenofth, divided into 100 links. 



SEC. II.] 



AREA OF GROUND. 



95 



is the measure in g-eneral use among snrve3'ors. In measuring 
land, the length of this chain is generally taken for the unit 
of linear measure. 

49. The unit of measure for surfaces is a square described 
on the unit of linear measure. 

1 foot. 



Thus, 1 square foot, 



1 square yard or 9 square feet, 



1 yard = 3 feet. 





















1 chain 


= 4 rods. 



































1 square chain, or 16 square rods. 



When, therefore, the linear measures are feet, yards, rods, or 
chains, the superficial measures, are square feet, square yards, 
square rods, or square chains; and the numerical expression 
for the area, is the number of times which the unit of superficial 
measure is contained in the land measured. 

50. Ais" Acre, which is the common unit of measure for 
land, is a surface equal in extent to 10 square chains; that is, 
equal to a rectangle of which one side is ten chains and the 
other side one chain. 

A EooD, is one quarter of an acre. 

Since the chain is four rods in lengtli, 1 square chain con- 
tains 16 square rods ; and therefore, an acre, which is 10 square 



ELEMENTS OF SURVEYING. 



[book II. 



chains, contains 160 square rods, and a rood contains 40 sqnare 
rods. A square rod is called a perch. 

51. Land is generally computed in acres, roods, and perches, 
which are respectively designated by the letters A. R. P. 

When the linear dimensions of a survey are chains or links, 
the area will be expressed in sqnare chains or square links, and 
it is necessary to form a rule for reducing such area to acres, 
roods, and perches. For this purpose, let us form the fol- 
lowing 

TABLE. 



Miles. 


Acres. 


Eoods. 


Sq. Chains. 


Perches. 


Sq. Links. 


1 


640 
1 


2560 
4 
1 


6400.0 

10.0 

2.5 

1.0 


102,400 

160 

40 

16 

1 


64,000,000 

100,000 

25,000 

10,000 

625 


] 


L squar 


3 mile = 


6400 squ[ 


ire chains = 


= 640 acres. 



When the linear dimensions are links, the area will be ex- 
pressed in square links, and may be reduced to acres by dividing 
by 100,000, the number of square links in an acre: that is, by 
pointing o^ five decimal places from the right hand. 

If the decimal part be then multiplied by 4, and five places 
of decimals pointed off, in the product, from Ihe right hand, the 
figures to the left will express the roods. 

If the decimal part of this result be now multiplied by 40, 
and five places for decimals pointed off, as before, the figures 
to the left will express the perches. 

If one of the dimensions be in links, and the other in chains, 
the chains may be reduced to links by annexing two ciphers: 
or, the multiplication may be made without annexing the 
ciphers, and the product reduced to acres and decimals of an 
acre, by pointing off three decimal places from the right hand. 



SEC. II.] AREA OF GROUND. * 97 

When both the dimensions are in chains, the product is 
reduced to acres by dividing by 10, or pointing off one decimal 
place. 

From which we conclude; that, 

1st. If linhs he multiplied ly linJcs, the x^rodiict is reduced 
to acres lij ^pointing off jive decimal places from the right hand. 

2d. If chains he multiplied hy linlcs, the product is reduced 
to acres ly pointing off three decimal places from the right 
hand. 

3d. If chains he multiplied ly chains, the product is reduced 
to acres ly pointing ojf one decimal place from the right hand. 

^% Since there are 16.5 feet in a rod, a square rod is equal 
to 16.5 X 16.5 = 272.25 square feet. 

If the last number be multiplied by 160, we shall have, 

272.25 X 160 = 43560 = the square feet in an acre. 

Since there are 9 square feet in a square yard, if the last 
number be divided by 9, we obtain, 

4840 = the number of square yards in an acre. 

PROBLEM I. 

53. To find the area of a piece of ground in the form of a square,*, 
rectangle, or parallelogram. 

EuLE. — Multiply the hase hy the altitude, and the product will 
express the area (Geom., Bk. IV., Prop. IV.) 

EXAMPLES. 

1. To find the area of the rectangular field JD 

ABCD. I 

Measure the two sides AB, EC: let us I 

suppose that we have found AB = 1^ chains j^ 

27 links, and BC=9 chains 75 links. Then, 



98 



ELEMENTS OF SUR^^YING. 

AB = 1427 links, 
BC= 975 links, 

AB X B0= 1391325 square links, 
= 13.91325 acres. 
4 



[book n. 



3.65300 roods, 
40 



26.12000 perches. 

A71S. 13 A. SB, 26 P. 

2. What is the area of a square field, of which the sides 
are each 33 ch. 8 1.? Ans. 109 A. IB. 29 P. 

3. What are the contents of a rectangular field, of which 
the longer side is 49 ch. 27 1., and the shorter 38 ch. 7 1.? 

A71S. 187 A. 2 B. 11 P. 

4. What are the contents of a field in the form of a 
parallelogram, of which the base is 35 ch. 65 L, and altitude 
,51 ch. 4 1. ? Ans. 181 A. 3 B. 33 B. 

PROBLEM II. 

54. To find the contents of a piece of land in the form of 
a triangle. 

FIRST METHOD. 

EuLE. — Measure either side of the 
triangle as BC, and from the oj^posite 
angle A, let fall a perpendicular AD, and 
measure this perpendicular ; then, mul- 
tiply the hase and perpendicular together, 
and divide the product ly 2 : tlie result loill express the area of 
the triangle. Or, the area is equal to tlie hase multiplied hj 
half the perpendicular, or to the perpendicular multiplied dy half 
the base (Geom., Bk. lY., Prop. YI.) 




SEC. II.] AREA OF GEOUND. 99 

EXAMPLES. 

1. What are the contents of a triangle whose base is 25 ch. 
11., and perpendicular 18 ch. 14 L ? "Ans. 22 A. 2 R. 29 P. 

2. What are the contents of a triangle whose base is 15.48 
chains, and altitude 9.67 chains? Ans. HA. IB. 38 P. 

SECOi^D METHOD. 

EuLE. — Measure tico sides and their included angle. Then, 
add together tlie logarithms of the two sides and the logarithmic 
sine of their included angle; from this sum subtract the logarithm 
of the radius, which is 10, and the remainder will de the logarithm 
of double the area of the triangle. Find, from the table, the 
number ansiuering to this logarithm, and divide it by 2: the 
quotient loill be the required area (Geom. Mens., Art. 96). 

EXAMPLES. 

1. In a triangle AB (7, suppose that we have found AB = 
57.65 ch., ^C— 125.81 ch., and the included angle CAB = 
57° 25' : required the area ? 

Let the required area be designated by Q; then, 

+ log AB 57.65 .... 1.760799 
+ log AC 125.81 .... 2.099715- 
+ log sin A 57° 25' .... 9.925626 
- log it 10 



log 2(2 



2Q = 6111.4 3.786140 

And Q = 3055.7 square chains. 

Ans. 305 A. 2 R. 11 P. 

XoTE. — In this example, the links are treated as decimal 
parts of the chain ; the result, therefore, is in square chains 
and decimal parts of a square chain. 



100 ELEMENTS OF SURYEYING. [BOOK n. 

2. What is tlie area of a triangle whose sides are 30 and 40 
chains, and their included angle 28° 57' ? 

A71S. 29 ^. i?. 7 P. 

THIRD METHOD. 

EuLE. — Measure the three sides of the triangle. Then, add 
them together and take half their sum. From this half sum 
subtract each side separately. Tlien, multiply the half sum and 
the three remainders together, and extract the square root of the 
product: the result tcill le the area (Geom. Mens., Art. 97). 

Or, after having obtained the three remainders, add together 
the logarithm of the half siwi and the logarithms of the respec- 
tive remainders, and divide their siwi by 2: the quotient will be 
the logarithm of the area. 

EXAMPLES. 

1. Find the area of a triangular piece of ground whose 
sides are 20, 30, and 40 chains. 

BY FIRST RULE. 

20 45 45 45 

30 -20. -30 -40 

40 25 1st rem. 15 2d rem. 5 3d rem. 



2)90 
45 = half sum. Then, 
45 X 25 X 15 X 5 = 84375: and V 84375 = 200.4737 = the 
area. Ans. 29^. OR. 8 P. 

2. What is the area of a triangle whose sides are 2569, 
4900, and 5035 links? 





BY SECOXD RULE. 


2569 


6252 6252 6252 


4900 


- 2569 - 4900 - 5035 


5035 


3683 1st rem. 1352 2d rem. 1217 


2)12504 




- 6252 = 


half sum. 



SEC. 11.] AKEA, OR CONTENTS OF GROUND. 101 



Then, 



log 6252 3.796019 

log 3683 3.566202 

log 1352 3.130977 

log 1217 3.085291 

2) 13.578489 
Area in square links, 6155225 . . . 6.789244 

Ans. 61 A. 2R. 8 P. 

PROBLEM III. 
55' To find the area of a piece of land in the form of a trapezoid. 

EuLE. — Measure the tivo parallel sides, and also tJie perpen- 
dicidar distance 'between them. Add the two parallel sides together, 
and tahe half the sum; then multiply the half sum hy the per- 
pendicular, and the product toill ie the area (Geom., Bk. IV., 
Prop. VII.) 

EXAMPLES. 



1. What is the area of a trapezoid, of 
which the parallel sides are 30 and 49 chains, 
and the perpendicular distance between them 
16 ch. 60 L, or 16.60 chains ? 

30 + 49 = 79 ; dividing by 2, giyes . . . 39.5 
multiply by 16.60 



area in square chains 655.700. 

Ans. 65^1. 2i?. IIP. 

2. Eequired the contents, when the parallel sides are 20 
and 32 ch., and the perpendicular distance between them 
26 ch. Ans. 67 A 2 P. 16 P. 

PROBLEM IV. 
56. To find the area of a piece of land in the form of a quadrilateral. 

Rule. — Measure the four sides of the quadrilatercd, and also 
one of the diagonals: the quadrilateral will thus le divided into 



102 



ELEMENTS OF SURYEYING. 



[book n. 



two triangles, in hoth of wliicli all tlie sides will le Icnomn. Tlien, 
find the areas of the triangles separately, and their sum tuill ie 
the area of the quadrilateral 



EXAMPLES. 

1. Suppose that we have measured 
the sides and diagonal AC, of the quad- 
rilateral ABCD, and found 

AB = 40.05 ch. CD = 29.87 ch., 
BG = 26.27 ch. AD = 37.07 ch., 
and AC = 55 ch. : 

required the area of the quadrilateral. 

A71S. 




101 A. IE, 15 P. 



Note. — Instead of measuring the four sides of the quadri- 
lateral, we may let fall the perpendiculars Bb, Dg, on the 
diagonal A C. The area of the triangle may then be determined 
by measuring these perpendiculars and the diagonal AC, The 
perpendiculars are Dg = 18.95 ch., and Bb = 17.92 ch. 

peoblem t. 

57. To find the contents of a field having any number of sides. 

EuLE. — Measure the sides of the field and also the diagonals : 
the three sides of each of the triangles into which the field will 
Ic thus divided will then be Icnoicn, and the areas of tlie triangles 
may then be calculated by the preceding rules. Or, measure the 
diagonals, and from the angular points of the field draiu perpen- 
diculars to the diagonals and measure their lengths : the base and 
p)erp)endicular of each of the triangles tvill then be Icnown, 



EXAMPLES. 



1. Let it be required to determine the contents of the field 
ABCDE, haying five sides. 



SEC. IL] 



AKEA OF GROUND. 



103 




Let us suppose that we have meas- 
ured the diagonals and perpendiculars, 
and found, 

AC = 36.21 ch., EC = 39.11 ch., 

Bb= 4.08 ch., Dd= 7.26 ch., 
A(f = 419 ch. : required the area of the field. 

Area of triangle ABC = 73.8684 square chains, 

area of " CDF = 141.9693 

area of " ACF = 81.7399 

area of ABCDE = 297.5776 " " 

Ans. 29 A. dB. IP. 




peoble:m ti. 

58. To find the contents of a long and irregular figure, bounded 
on one side by a straight line. 

Suppose the ground, of -which the contents are required, to 
be of the form ABEeda, bounded on one side by the right line 
AE, and on the other by the curve edca. 

At A and E, the extremities of the 
right line AE, erect the two perpen- 
diculars Aa, Ee, and on each of them A B O D 
measure the breadth of the land. Then diyide the base into 
any convenient number of equal parts, and measure the breadth 
of the land at each point of division. 

Since each part of the entire area, as ABha, is a trapezoid 
having an equal altitude — viz., the equal distance between any 
two of the perpendiculars ; and since the area of each trapezoid 
is equal to half the sum of its parallel sides multiplied by the 
distance between them; and since the sum of these areas make 
up the area of the whole figure; and since, in this sum, each 
perpendicular, except the extreme ones, is taken twice and they 
but once; and since the distance between any two perpendiculars 



104 ELEMENTS OF SURVEYING. [BOOK II. j 

] 

is a common multiplier of each part; therefore, for the entire , 
area, we have the following ^ \ 

EuLE. — Add togetJier the intermediate Ireadtlis and half the \ 
sum of the two extreme ones: then midtiply this sum hy one 
of the equal parts of the lase-line, and the product luill le the ' 
required area very nearly. ' 

I 

EXAMPLES. \ 

1 

1. The breadths of an irregular figure, at five equidistant j 
places, being 8.20 ch., 7.40 ch., 9.20 ch., 10.20 ch., and 8.60 j 

chains, and the whole length 40 chains, required the area. \ 

\ 

8.20 4)40 i 

8.60 10 one of the equal parts. \ 

2 )16.80 \ 

8.40 mean of the extremes, 35.20 sum, ' 

7.40 10 I 

9.20 area 352.00 square ch. \ 
10.20 



35.20 sum. 

Ans. 35^. 32 P. 

2. The length of an irregular piece of land being 21 ch., 
and the breadths, at six equidistant points, being 4.35 ch., 
5.15 ch., 3.55 ch., 4.12 ch., 5.02 ch., and 6.10 chains: required 
the area. Ans, ^ A, %B. 30 P. 

3. The length of an irregular piece of land is 80 ch., and 
the breadths at nine equidistant points are 5.75 ch., 6.12 ch., 
4.80 ch., 5.09 ch., 3.87 ch., 5.17 ch., 6.00 ch., 3.94 ch., and 5.95 
ch.: what is the area? Ans. 40.4. 3 P. 14 P. 

4. The length of an irregular field is 39 rods, and its 



SEC. II.] 



AREA OF GROUND. 



105 



breadths at five equidistant places are 4.8, 5.2, 4.1, 7.3, and 7.2 
rods: what is its area? A^is. 220.35 sq. rods. 

Note. — If it is not convenient to erect the perpendiculars 
at equal distances from each other, the areas of the trapezoids, 
into which the whole figure is divided, must be computed sepa- 
rately: their sum will be the required area. 

PR0BLE3I YII. 



59. To find the contents when the boundary is an irregular Kne. 

It frequently happens that a plot to be surveyed is bounded 
partly by an irregular line. In such a case, one or more 
straight lines are surveyed, and offsets measured from these 
lines, as often as may 
be required to afford 
data for the computa- 
tion of the area, and 
a true delineation of 
the boundarv. In the 

case represented in "■'''^ ■'' '" '"^ 

the figure, the stream 
from A to C is the 
boundary. The sta- 
tion B is selected for 
convenience, as it is 
evident, if the line were run direct from A to 6', the labor of 
taking the offsets would be much greater. 

It will be observed that the offsets are so measured as to 
indicate the abrupt bends in the boundary; and furthermore, 
so that the areas thus cut off may be considered as being bounded 
by straight lines, without sensible error. 




106 



ELEMENTS OF SURVEYING. 



[BOOK II. 



60. When the honnd- 
ary is a crooked stream 
that is easily crossed, it 
is often conyenient to 
survey a line across the 
bend, as in the figure, 
and locate by offsets 
upon both sides of the 
line. In any case, the 
small areas to be com- 
j)uted are only trape- 
zoids and triangles. 




PEOBLEM Tin. 
61. To find the area of a piece of ground in the form of a circle. 



EuLE. — Measure the radius AG: then 
miiltiphj the square of the radius hy 
3.1416 (Mens., Art. 105). 



To find the area of a circular piece of land, of which the 
diameter is 25 ch. Ans. 4:9 A. E. 14: P. 




PEOBLEM IX. 



62. To find the contents of a piece of ground in the form of 

an ellipse. 



EiJLE. — Pleasure the semi-axes AE, CE. 




Tlieii multijily them together, and their 
product hy 3.141^. 



To find the area of an elliptical piece of ground, of 
which the transverse axis is 16.08 ch., and the conjugate 
axis 9.72 ch. Ans. 1%A.1R.4:P, 



SEC. III.] COMPASS SUKYEYING. 107 

Note 1. — The following is tlie manner of tracing an ellipse 
on the ground, when the two axes are known. 

From G, one of the extremities of the conjugate axis as a 
centre, and AE, half the transverse axis, as a radius, describe 
the arc of a circle cutting AJS in the two points F and G : 
these points are called the foci of the ellipse. 

Then, take a tape, the length of which is equal to AB, 
and fasten the two ends, one at the focus F, the other at the 
focus G. Place a pin against the tape and moye it around, 
keeping the tape tightly stretched: the extremity of the pin 
will trace the curve of the ellipse. 

XoTE 2. — In determining the contents of ground, in the 
examples which have been given, the linear dimensions have 
been taken in chains and decimals of a chain. 

If the linear dimensions were taken in terms of any other 
unit, they may be readily reduced to chains. For, a chain is 
equal to 4 rods, equal to 22 yards, equal to QQ feet. Hence, 

1st. Rods may le reduced to chains and the decimal of a 
chain, by dividing ly 4. 

2d. Yards may le reduced to chains and the decimal of a 
chain, hy dividing ly 22. 

3d. Feet may le reduced to chains and the decimcd of a 
chain, hy dividing ly ^Q. 

XoTE 3. — If it is thought best to calculate the area, with- 
out reducing the linear dimensions to chains, the result can 
be reduced to acres: 

1st. By dividing it ly 160, luhen it is in square rods 
(Art. 50). 

2d. By dividing it ly 4840, luhen it is in square yards 
(Art. ^2). 

3d. By dividing it ly 43560, 2vhen it is in square feet 
(Art. 52). 



108 



ELEMENTS OF SURVEYING. 



[book n. 



SECTION III. 



COMPASS SURVEYING, 



63. The Axis of the earth is the immovable diameter about 
which it revolves; and the poles are the points in which the 
axis meets the surface. 

64. Any plane passing through the axis of the earth is called 
a meridian plane ; and its intersection with the surface is called 
a meridian line, or simply a meridian. 

65. All the meridians converge towards the poles, but they 
vary so little from parallelism, within the narrow limits of 
surveys made with the compass, that they may, without sensible 
error, be regarded as parallel straight lines. 

66. If a magnetic needle be suspended freely, and allowed to 
settle to a state of rest, a vertical plane passed through its axis 
is called the plane of tlie magnetic meridian ; and its intersec- 
tion with the surface of the earth is called the magnetic meridian, 
or sometimes, a North and South line. A line perpendicular to 
a North and South line, is called an East and West line. 

67. A line traced, or measured on the ground, is called a 
Course; and the angle which this line makes with the magnetic 
meridian, passing through the 
point of beginning, is called the 
Bearing. 

Thus, if we start from the 
point A, and measure in the di- 
rection AB, the line AB is the 
course, and the angle NAB, is 
the bearing. 

When the course, like AB, falls between the north and east 




SEC. m.] COMPASS SUKVEYING. 109 

points, and makes an angle of 46° with the meridian, the bearing 
is read, north 46° east, and is written, N. 46° E. 

When the course, like AC, falls between the north and west 
points, and makes with the meridian an angle of 30°, the bearing- 
is read, north 30° west, and is written, X. 30° W. 

When the course, like AD, falls between the south and west 
points, and makes an angle with the meridian of 70°, the bearing 
is read, south 70° west, and is written, S. 70° W. 

When the course, like AF, falls between the south and east 
points, and makes with the meridian an angle of 70°, the bearing 
is read, south 70° west, and is written, S. 70° W. 

A course which runs due north, or due south, is designated 
by the letter N, or S ; and one which runs due east, or due west, 
by the letter E, or W. 

68. If, after having passed over a course, the bearing is taken 
to the back station, this bearing is called the bach sight, or reverse 
hearing. 

69. The perpendicular distance between the east and west 
lines, drawn through the extremities of a course, is called the 
northing or southing, according as the course is run towards the 
north or south. This distance is also called the difference of 
latitude, or simply the latitude, because it shows the distance 
which one end of the course is north or south of the other. 

Thus, in running the course from A -^ 

to B, AC is the difference of latitude, C—^^-r-'j^ 

north. ^ -:^r \ 

^ — E 



70. The perpendicular distance between ^ 
l5he meridians passing through the extremi- 
ties of a course, is called the depart^ire of 
that course, and is east or west, according 
as the course lies on the east or west side of the meridian passing 
through the point of beginning. 

Thus, in running the course AB, CB is the departure, east. 



110 ELEMENTS OP SURVEYING. [BOOK II. 

71. It is found couvenient, in explaining the rules for sur- 
veying with the compass, to attribute to the latitudes and 
departures, the algebraic signs, + and — . 

We shall, therefore, consider every northing as affected with 
the sign +, and every southing as affected with the sign — . 
We shall also consider every easting as affected with the sign -}-, 
and every westing as affected with the sign — . 

72. The meridian distance of a point is its perpendicular 
distance from any assumed meridian. Thus, if the distance be 
estimated from the meridian NS, BC will be the meridian dis- 
tance of the point B. 

73. The meridian distance of a line, is the meridian distance 
of its middle point, and is east or west, according as this point 
lies on the east or west side of the assumed meridian. Thus, 
FG drawn through the middle point of AB, is the meridian 
distance of the line AB. 

The sign + will always be given to the meridian distance 
of a point or line, when it lies on the east of the assumed 
meridian, and the sign — , when it lies on the west. 

Suevetoe's Co:5ipass. 

71. This instrument (PI. 2, Eig. 2), consists of a compass-box 
DCE, a magnetic needle, a brass plate AB, from twelve to four- 
teen inches long, two plain sights, AF and BG, one of which 
is more fully shown in Fig. 3 ; and a stand, which is sometimes 
a tripod, and sometimes a single staff pointed with iron at the 
lower end, so that it may be placed firmly in the gi'ound. 

The open sights, AF and BG, are placed at right angles to 
the plate AB, and fastened to it firmly by the screws a and 1), 
In each sight there is a large and small aperture or slit; the 
larger aperture being above the smaller in one of the sights, 
and below it in the other. A hair or thread of silk is drawn 



SEC. III.] COMPASS SUEVEYING. Ill 

vertically through the middle of the large aperture, as showu 
in Eig. 3. 

The compass-box DGE is circular, and generally about six 
inches in diameter. At the centre is a small pin, on which the 
magnetic needle is poised. This needle, if allowed to turn freely 
around the point of support, will settle to a state of rest: 
the direction which it then indicates, is that of the mag7ieUc 
meridian. 

In the interior of the compass-box, there is a graduated 
circle divided to degrees, and sometimes to half degrees : the 
degrees are numbered from the extremities of the diameter NS, 
both ways to 90°. 

The length of the magnetic needle is a little less than the 
diameter of the graduated circle, so that the needle can move 
freely around its centre, within the circle, and its positions be 
noted on the graduated arc. 

The compass-box is turned about its centre, without moving 
"the plate AB, by means of the milled screw L: and is fastened 
to the plate AB, by the screw P. 

In using the compass, it is important to ascertain the exact 
angle which may be included between the magnetic meridian 
and the course. The course is always indicated by the line 
drawn through the eye and the sights AF and BQ. 

To measure this angle, accurately, a small arc HI is described 
on the bar J. jS, having its centre at the centre of the compass-box. 
This arc is divided to degrees, and sometimes to the parts of a 
degree. A vernier is also used, which is permanently attached 
to the compass-box. 

When the point of this vernier coincides with the point 
of the graduated arc HI, the line of the compass-box marked 
NS, lies in the plane of the sights. 

Suppose the of the vernier to coincide with the of the 
arc HI If the end of the needle does not stand at one of the 



112 



ELEMENTS OF SURYEYING. 



[book II. 



lines of division of the graduated circle, let the whole degrees 
be read. Then, turn the compass-box by means of the screw Z, 
until the needle points exactly to the line Avhich marked the 
whole degrees: the space passed over by the of the vernier, 
shows the parts of a degree that are to be added, to give the 
true reading. 

Work ojs^ the Field. 

75. When a piece of ground is to be surveyed, we begin at 
some prominent corner of the field, and go entirely around the 
land, measuring the lengths of the bounding lines with the 
chain, and taking their bearings with the compass. It is not 
material whether the ground be kept on the right hand or on 
the left, and all the rules deduced for one of the cases, are 
equally applicable to the other. To preserve uniformity, however, 
in the language of the rules, we shall suppose the land to be 
always kept on the right hand of the 
surveyor. 

Let ABCD be a piece of ground 
to be surveyed, A the point where 
the work is to be begun, and NS a 
meridian. 

On a sheet of paper, rule three 
columns, as follows, and head them 
stations, bearings, distances. 




stations. 


Bearings. 


Distances. 


1 

2 
3 
4 


N 31i° W 
N 62° E 
S 36° E 
S 45i°W 


10.40 
9.20 
7.60 

10.00 



Place the compass at A, and take the bearing to B, 
which is FAB: suppose this angle has been found to be 31|°. 



SEC. III.] COMPASS SUKYEYING. 113 

The bearing from ^ to i? is then K. 31|-° W. Enter this bearing 
in the field notes opposite station 1. Then measure the distance 
from A to B, which we will suppose to be 10 ch. 40 L, and insert 
that distance opposite station 1, in the column of distances. 

We next take the bearing from B to C, jN". 62° E., and then 
V measure the distance BC = 9 ch. 20 1., both of which we insert 
in the notes opposite station 2. 

At station C we take the bearing to D, S. 36° E., and then 
measure the distance CD = 7 ch. 60 1., and place them in the 
notes opposite station 3. 

At D we take the bearing to A, S. 45^° W., and measure 

the distance DA = 10 ch. "We shall then have made all the 

measurements on the field which are necessary to determine 
the contents of the ground. 

Principles. 

76. The reverse-bearing or back-sight, from B to A, is the 
angle ABE ; and since the meridians NS and EG are parallel, 
this angle is equal to the bearing NAB. The reyerse-bearing 
is, therefore, S. 31^° E. 

The reyerse-bearing from C, is S 62f ° W. ; that is, it is the 
angle ICB = GBC. And generally, 

A reverse-hearing, or hack- sight, is aliuays equal to the for^- 
tuard-'bearing, and differs from it only i7i loth of the letters ly 
vMch it is designated. 

77. In taking the bearings with the compass, there are two 
sources of error. 1st. The inaccuracy of the obseryations : 2d. 
Local attractions, or the derangement which the needle expe- 
riences when brought into the yicinity of iron-ore beds, or any 
ferruginous substances. 



114 



ELEMENTS OF SURVEYING. 



[book II. 




To guard against these sources of error, the reyerse-bearing 
should be taken at every station : if this and the forward- 
bearing are of the same value, the work-is probably right; but 
if they differ considerably, they should both be taken again. 

78. In passing over the course 
AB, the northing is found to be HB, 
and the departure, which is west, is 
represented by AR. Of the course 
BC, the northing is expressed by BG, 
and the departure, which is east, by 
GO. Of the course CD, the southing 
is expressed by CI, and the departure, 
which is east, by CF. Of the course 
DA, the southing is expressed by KA, 
and the departure, w^hicli is west, by DK. It is seen from the 
figure, that the sum of the northings is equal to RB + BG = 
HG J and that the sum of the southings is equal to CI + XA 
= PA = RG : hence, the sum of the northings is equal to the 
sum of the southings. 

If we consider the departures, it is apparent that the sum 
of the eastings is equal to GC + CF — GF ; and that the sum 
of the w^estings is equal to AH -\- DK — GF: hence, the sum 
of the eastings is equal to the sum of tlie westings. "We there- 
fore see, that when the survey is correct, the sum of the northings 
luill te equal to the sum of the southings, and the sum of the 
eastings to the sum of the westings. 

It would, indeed, appear plain, even without a rigorous 
demonstration, that after having gone entirely round a piece 
of land, the distance passed over in the direction due north 
must be equal to that passed over in the direction due south ; 
and that the distance passed over in the direction due east 
must be equal to that passed over in the direction due west. 

79. The boundaries of a field are generally occupied by 



SEC. III.] 



COMPASS SUKVEYTNG. 



115 



fences, and frequently also by a border of shrubbery, so that 
chaining along the true boundary is impossible. 

In such cases, it becomes necessary to measure an oifset at 
each end of the course (and at right angles to 
it), and of sufficient length to clear the obstruc- 
tions ; the measurement is then made between 
these temporary stations. 

It is evident that the bearing and length of 
inUf the ofiset-course, are the same as those 
of J/3\ 

When such offset-courses are necessary for several 
successive courses, errors are likely to be committed, 
unless the surveyor is careful to make new offsets 
for each course. 






M 


/s 


t' 


r'i 


^ 




iS, 


V 


:p 


\. 


5^ 




^ 




vs 


% 




.--' 


'^.rf 




'■'^' 


/l 


V '• 


'-,--. 


'■\ 




^■' 


•,r; 


M 


r- 


yy 



?> 



jsr 



The offset-courses, for the lines LM, MN, and 2s 0, are re- 
spectively Im, m'n, and )iJ^ 



JST 













0< 



Such offsets, in field surveys, may generally be measured by 
the flag-staff, and the right angle may be determined with 
sufficient accuracy by the eye. 

It is, of course, immaterial, so far as accuracy is concerned, 
upon which side of the line the offset is taken, whether it be 
outside or inside the field. 



116 ELEMENTS OF SURVEYING. [BOOK II. 

80. It has been customary, since the first settlement of this 
country, to use the compass in all land surveys, so that the 
description of lands, in purchase and sale, and by which they 
are recognized in the courts, inyolves the length and bearing 
of each straight line of the boundary. The method, therefore, 
is, at present, a necessary one. 

The errors to which the compass is liable are so numerous 
and so yariable, eyen in the same instrument, tliat a change 
of practice is yery desirable. Many surveyors, to insure a higher 
degree of accuracy, measure the angles of a field with the 
theodolite or transit, and then, haying determined the bearing 
of one side w^ith sufficient accuracy, calculate the others by a 
method to be shown in a subsequent article. 

81. In surveys of large areas, the surveying party should 
consist of at least four persons — viz., a compass-man, a flag- 
man, and two chain-men. In smaller areas, the work is gen- 
erally performed by the surveyor and one assistant ; the surveyor 
serving alternately as compass-man and hind-chainman, and 
the assistant as flag-man and fore-chainman. 

82. The best method of recording the notes of the survey 
of any line, from which numerous ofi*sets are measured, is to 
record the distances along the line in a central column of the 
left-hand page of the note-book, beginning the record at the 
bottom of the page, and reserving each right-hand page for a 
diagram of the survey, and such remarks as are necessary. 

The advantage of beginning at the bottom of the page is 
this: that when standing on the line to be surveyed, and look- 
ing in the direction we propose to go, the column in the book 
lies before us just as the line does, and all measurements made 
to the right or left of the line are recorded at the right or left 
of the column. In surveys where many auxiliary notes are 



SEC. m.] COMPASS SUEYEnNG. 117 

taken, a diagram is an important aid to a ready interpretation 
of the other notes. 



Gexeral Example. 

83. To explain the method, in full, of making a compass 
survey and recording the notes, ^e will take an example of a 
farm, in which, in addition to the usual survey of the boundary, 
snch other measurements are made as to enable us to make a 
correct map of the whole. 

Page 119, represents a farm to be sui*veyed, and page 11 S, the 
notes which are made, in the operations on the field. 

Beginning with the comer marked A, the bearing of the 
line AB, is taken. In most cases, oflTsets from both A and B 
would be taken, in order that the survey may be clear of the 
fence, but such ofi'sets are not recorded. 

The record of the bearing of the first course is entered at the 
right of the column (page 118), while the letter designating the 
station, is placed to the left. 

The symbol A. which signifies station, is placed in the 
column, between the letter and the bearing, for each angle of 
the farm. 

In chaining the first course, the intersection of the line 
with any objects worthy of notice is recorded. The first record 
is of the road leading to the quarry. As it is an unimportant 
road, a single measurement of the distance on the course to its 
centre is sufficient to locate it. The distance is 1.30 chains. 

At 11.30 and 12.35 the sides of the turnpike are intersected. 
The bearing of the road, at this point, is also carefully taken and 
recorded. 

The intersections of the Garden fence and of the Brook are 
also noted (17.40) and (18.10) ; and these, with the entire length 
of the course (31.95), close the record of this line. 



to Station A 
FenceN6GhtW 



S~¥'l- ^^^^ ,''' OAK T REIT 

,.0v' IN FAST SIDE 




Slfdion A 



2i- (^S^S^IAT 



MAP OF FAIUI. 




120 ELEMENTS OF SUETEYES-G. [BOOK H. 

At B, the bearing of the northernmost chimney of the farm- 
honse is taken (X. T3° E.) Such bearings serre two purposes. 
They aid in the location of the objects observed, npon the map, 

and serve also, in case of errors, to aid in detecting their 
location. 

In general, in surveying large or small areas, some prominent 
point or points, Tvithin the botmdary, should be selected, and 
their bearings, from different angles, carefully noted. 

The chimney of the farm-house and the oak-tree in the 
comer of the wheat-field, are thus employed in this survey. 

At C, the corner of the field, is in the centre of the brook, 
and from this point to D, the brook is the boundary. A straight 
line is run between the stations, and offsets are measured to 
each bend of the brook. 

It is necessary, in such a case, for the chainmen to exercise 
unusual care in keeping in the line between the stations, other- 
wise the lengths of the offeets cannot be correctly measured. 

At E, the bearing of the oak-tree is taken (INT. 1^° E.) On 
the course between E and F, a marsh is encountered, which the 
chainmen pass,. by an oflfeet course. 

At F, another beai-ing is taken of the oak-tree (S. 44^' E.) 

At G, the bearing of the farm-house chimney is noted 
(S. 26° E.) At G and H the bearings of the division-fences are 
taken. On the cotirse from H to J, the turnpike is again crossed : 
the intersection of both sides, together with the beating, are 
carefully noted. 

From / to K, the intersection and bearing of the fence be- 
tween the potato and the wheat field, are recorded. The course 
from jST to J. closes the survey. 

To locate the buildings about the farm-house, a few measure- 
ments would be necessary; but they may begin with the point 
already located by the bearings taken — the chimney nearest the 
north end of the house. 



SEC. III.] COMPASS SURVEYING. 121 

The dimensions of the buildings, their distances apart, and 
the direction of one side of each being taken, sufficient data is 
afforded for locating them, correctly, upon the map. 

K"0TE. — The advantage of the compass over other instruments 
with which angles are measured, lies chiefly in this: that the 
Bearing of a course may be measured at any point on the 
line. 

When the angle between adjacent sides is taken with the 
Transit or Theodolite, the work can only be done at the corners 
of the field; and when, as frequently happens, a hill intervenes 
between two consecutive stations, it becomes necessary to locate 
a point on the hill, in the true line, and then return to the 
corner to measure the angle ; whereas, when the compass is 
employed, the establishment of the intermediate point on the 
hill aflibrds the means of taking the proper bearing without 
going to the angle. Furthermore, the bearings may be meas- 
ured with the compass, by placing it at the alternate stations 
only. 

COXTEXTS OF GkOUXD. 

84. Haying explained the necessary operations on the field, 
we shall now proceed to show the manner of computing the 
contents of ground. 

THE TEAVERSE TABLE AXD ITS USES. 

85. This table shows the latitude and departure corre- 
sponding to bearings that are expressed in degrees and quarters 
of a degree, from to 90°, and for every course from 1 to 100, 
computed to two places of decimals. 



The followins: is the method of deducing the formulas for 



■to 
computing a traverse table; by means of these formulas and a 

6 




122 ELEMENTS OF SURYEYEs'G. [BOOK H. 

table of natural sines, the latitude and departm-e of a course 
may be computed to any desirable degree of accuracy. 

Let AD represent any course, and 
XAD — ACB, expressed in degrees and 
minutes, be its bearing. Let AC be the 
unit of measure of the course, and also 
the radius of the table of natural sines 
(Bk. L, Sec. III., Art. 14). Draw DE and ^ 
CB parallel to XS, and AE perpendicular 
to AS, Then will DE be the latitude, and AE the departure 
of tlie course, and CB the cosine, and AB the sine of the 
hearing, to the radius AC=1. 

From similar triangles we have these proportions, 

AC \ CB w AD : DE, or 

1 : cos of the bearing : : course : latitude; 

and AC \ AB w AD \ AE, or 

1 : sin of the bearing : : course : departure. 

Whence, lat. = course X cos of the bearing, 
dep. = course X sin of the bearing. 

We have then the following practical rule for computing 
the latitude and departure of any course. 

Look in a tahle of natural sines for tJie cosine and sine of 
the bearing. MuUipJif each ty the length of the course, and the 
first product icill le the latitude, and the second will he the 
departure of the given course. 

EXAMPLES. 

1. The bearing is 65^ 39', the course 69.41 chains: what 
is the latitude, and what the departure? 



SEC. III.] COMPASS SURVEYING. 123 

Natural cosine of 65° 39' 41231 

Length, of the course 69.41 

Product, which is the Dif. of Lat. . . 28.6184371 

Natural sine of 65° 39' .91104 

Length of the course . 69.41 

Product, which is the Departure . . 63.2352864 

2. The bearing is 75° 47', the course 89.75 chains: what 
is the latitude, and' what the departui-e? 

Natural cosine of 75° 47' 24559 

Length of course 89.75 

Product, which is the Dif. of Lat. . . 22.0417025 

Natural sine of 75° 47' 96937 

Length of course 89.75 

Product, which is the Departure . . 87.0009575 

In this manner, the traverse table given at the end of the 
book, has been computed. When the bearing is given in 
degrees and quarters of a degree, and the difference of latitude 
and departure are required to only two places of decimals, they 
may be taken directly from the traverse table. 

When the bearing is less than 45°, the angle will be 
found at the top of the page; when greater, at the bottom. 
When the distance is less than 50, it will be found in the column 
"distance,'' on the left-hand page; when greater than 50, in 
the corresponding column of the right-hand page. 

86. The latitudes or departures of courses IN 



of different lengths, but which have the 
same bearing, are proportional to the ...^ 



lengths of the courses. Thus, in the ^ 

figure, the latitudes AG, AC, or the de- 
partures GF, CB, are to each other as the g 
courses AF, AB, 



..... 



-vF 



E 



124 ELEMENTS OF SURVEYING. [BOOK H. 

Therefore, when the distance is greater than 100, it may be 
divided by any number which will give an exact quotient, less 
than 100 : then the latitude and departure of the quotient being 
found and multiplied by the divisor, the products will be the 
latitude and departure of the whole course. It is also plain, 
that the latitude or departure of two or more courses, having 
the same bearing, is equal to the sum of the latitudes or depart- 
ures of the courses taken separately. 

Hence, if we have any number greater than 100, as 614, we 
haye only to recollect that, 610 + 4= 614; and also, that the 
latitude and departure of 610, are ten times .as great, respectively, 
as the latitude and departure of 61 : that is, equal to the latitude 
and departure of 61 multiplied by 10; or, to such latitude and 
departure with the decimal point removed one place to the 
right. 

EXAMPLES. 

1. To find the latitude and departure for the bearing 29|-°, 
and tlie course 614. 



Latitude for 610 . . . 530.90 
Latitude for _f • • • 3.48 
Latitude for 614 .. . 534.38 



Departure for 610 . . 300.40 
Departure for 4 . . 1.97 
Departure for 614 . . 302.37 



In this example, the latitude and departure answering to 
the bearing 29-1-°, and to the distance 61, are first taken from 
the table, and the decimal point removed one place to the right : 
this gives the latitude and departure for the distance 610; the 
latitude and departure answering to the same bearing and the 
distance 4, are then taken from the table and added. 

2. To find the latitude and departure for the bearing 62|°, 
and the course 7855 chains. 

Latitude for 7800 . 3602.00 | Departure for 7800 . 6919.00 
Latitude for 55 . 25.40 Departure for 55 . 48.79 
Latitude for 7855 . 3627.40 | Departure for 7855 . 6907.70 



SEC. III.] 



COMPASS SUEVEYING. 



125 



]NoTE. — When the distances are expressed in "whole numbers 
and decimals, the manner of finding the latitudes and departures 
is still the same, except in pointing ofi" the places for decimals : 
but this is not difficult, when it is remembered that the column 
of distances in the table, may be regarded as decimals, by 
simply removing the decimal point to the left, in the other 
columns. 

3. To find the latitude and departure for the bearing 47f°, 
and the course 37.57. 



Latitude for 37.00 . . 24.88 
Latitude for _^ . . .38 
Latitude for 37.57 . . 25.26 



Departure for 37.00 • . 27.39 
Departure for .57 . .42 

Departure for 37.57 . 27.81 



bala:s'ciis"g the woek. 

87. Having explained the use of the traverse table, we can 
proceed to compute the area of the ground. 

The field-notes having been completed, rule a new table, as 
on next page, with four additional columns, two for latitude, 
and two for departure. 

Then find, from the traverse table, the latitude and de- 
parture of each course, and enter them in the proper columns 
opposite the station. 

Then add up the column of northings, and also the column 
of southings : the two sums should be equal to each other. 
If they are not, subtract the less from the greater ; the remain- 
der is called the erro?' i?i latitude. This error takes the name 
of that column which is the least. For example, if the sum 
of the northings is less than the sum of the southings, the 
error is called, eiTO?' in northing : but if the sum of the southings 
is less than the sum of the northings, the error is called, e7T0?' 
in southing. And similarly for the departures. 



126 



ELEMENTS OF SURVEYING. 



[book II. 



This error for liiLitude or departure must be distributed 
among tlie latitudes or departures of all the courses, in pro- 
portion to the length of each course, observing to add the 
correction, when applied to the deficient column, and to sui- 
tract it, when applied to the other. 

We will illustrate this, by the example of (Art. 75). 



stations. 


Bearings. 


Dis. 


Dif. Lat. 


Dep. 


Balance. 


+ 


S. 


E. 

+ 


W. 


1 
Lat. Dep. 


1 


n; 31F w. 


10.40 


8.87 






5.43 


+ 8.86 


-5.44 


2 


1^.62° E. 


9.20 


4.32 


.... 


8.13 




+ 4.31 


+ 8.12 


3 


S. 36° E. 


7.60 




6.15 


4.47 




-6.15 


+ 4.46 


4 


S. 451-° W. 


10. 




7.01 




7.13 


-7.02 


-7.14 


Sum of angles, 37.20 


13.19 


13.16 


12.60 


12.56 








13.16 




12.56 









Error in southina* . . . 



.03 



.04 



Error in westing. 



The error in southings, 3 links, is to be distributed among 
the northings and southings, in proportion to the lengths of 
the courses; a part to be added to the southings, and the 
remaining part subtracted from the northings. The error in 
westings is similarly distributed among the eastings and west- 
ings. Eor this, two new columns are formed, called, the iaJanced 
latitudes and departures ; and to these columns the latitudes 
and departures are transferred, after the corrections have been 
made: the north latitudes being marked +, and the south lati- 
tudes — , in order to distinguish them readily, and also, for 
convenience in the calculations which follow. 

The error of .03 in the latitudes is distributed among the 
latitudes, by subtracting 1 link from the northings of courses 
1 and 2, and adding 1 link to the southing of course 4. This 
produces a balance. 



SEC. m.] COMPASS SURVEYING. 127 

Of the error of 4 links in the departures, 1 link is added to 
each of the departures west, and 1 link subtracted from each 
of the departures east. This produces a balance. 

XoTE. — When a knowledge of the conditions under which 
tlie survey was made, enables us to determine that errors were 
more likely to occur at certain points, it is doubtless best to 
apply the corrections to those courses where it seems probable 
the errors were made. 

88. The limit of error, to be allowed, depends of course upon 
the importance of the survey. 

In ordinary farming districts, the error should be as small 
as 1 link to 5 or 10 chains of perimeter. 

The '*' error of the survey" should be considered as the length 
of the line necessary to close the 'boundary, and is equal to the 
square root of the sum of the squares of the errors of latitude 
and departure. Thus, in the above example, the error of the 
survey is 5 links. The perimeter being 37.20 chains, the error 
is about 1 link to T.io chains, or ^-g- of the perimeter. 

89. It will be well to bear in mind the fact, that if the 
error in the perimeter has been made in one course only, and 
distributed by tlie ordinary methods of balancing, among all the 
courses, the error in area will be larger than the error in 
perimeter. 

90. When the error is so large that a re-survey becomes 
necessary, the balancing should be carefully re-examined. 

In many cases, the location of the error may be determined 
by inspection of the computation, and a portion of the labor 
of a re-survey, thereby saved. 

This refers more particularly to those cases where the error 
is one of chaining, and is mostly in one course. Errors of this 
kind occur sometimes with experienced chainmen, who draw 



128 ELEMENTS OF SUEVEYING. [BOOK II. 

the chain properly between the courses, but make occasionally 
an error in counting the fractional part of a chain at the end 
of a course. 

In such cases, the location of the error may be detected by 
observing first what columns contain errors, and secondly the 
ratio of the errors of Latitude and Departure. 

When the error in the survey has been a single one, of dis- 
tance only, then the ratio between the errors of Latitude and 
Departure must be the same as the ratio between the Latitude 
and Departure of the course to be corrected. If the errors be 
in northings and westings, then the courses running either 
Xorth and West, or South and East, should be examined. 

01. The surveyor should take every possible precaution 
against errors in the bearings. This is accomplished by back- 
sighting, taking bearings of some one object from several sta- 
tions, and also by taking bearings of stations across the field. 
These precautions will give, in general, sufficient data for the 
detection of an error in hearing ; for, by mapping the survey, 
and drawing the lines to indicate the extra bearings, the error 
is revealed by the failure of the lines to meet at a common 
point. 

92. One source of error, in large surveys with the compass, 
is frequently overlooked. This is the diurnal variation : there 
is sometimes as much as 15 minutes variation during the day- 
light hours. 

Errors from this source can only be avoided by testing the 
compass, at intervals of two or three hours, by taking the 
bearing of the same line. 

93. If each of the angles of the survey, included between 
two consecutive courses, be calculated by the method explained 
in Article 000, the bearings may then be verified by comparing 



SEC. m.] AEEA OF GEOUXD. 129 

the sum of these angles -with, the sum of the interior angles 
of any polygon (Leg., Bk. I., Prop. 25). The same verification 
may also be made when the angles are measured with the 
theodolite or transit. 

94. There is one kind of error frequently made in reading 
^ the compass when the bearing is nearly east or west. The 

error arises from reading Xorth for South, or the reverse. If 
the survey is otherwise correct, the error in latitude is just 
twice the latitude of the course containing the error. 

Double Meeidia^^ Distances. 

95. After the work has been balanced, the next thing tO' 
be done is to calculate the double meridian distance of each 
course. 

For this purpose, any meridian line may be assumed. It is,, 
however, most convenient to assume that meridian which passes 
through the most easterly or westerly station of the surveys 
and these two stations are readily determined by inspecting 
the field-notes. 

Having chosen the meridian, let the station through which 
it passes be called the princijoal station, and the course which 
begins at this point, the first course. Care, lioiuever, must be talcen,. 
not to confound this with the course which hegins at station 1,. 
and luhicli is the first course that is entered in the field-notes. 

It has already been remarked (Art. 71), that all departures 
in the direction east are considered as plus, and all departui'es 
in the direction west as minus. 

96. To dedtice a rule for finding the dotible meridian dis^ 
tance of any course. Let SX be the assumed meridian. Let 
jB (7 represent any course, and AB the preceding course; also, 
let D and E be their middle points. Draw EH, Z>6^, and CM, 



130 



ELEMENTS OF SURVEYING. 



[book n. 



perpendicular to the assumed meridian 
]^S. Draw also J/, BX, and BL, par- 
allel to XS. Then 2DG is the double 
meridian distance of the course BC, and 
'ZBB=2KG, is the double meridian dis- 
tance of the course AB. 

Xow, WG=2 GK + '2EL -f 2LD ; but 
2KL = IL is the departure of the course 
AB, and %LB — MC is the departure of 
the course BC : ' 



N 



H 




M a 



consequently. 



2GD = 2GK -{- IL + MC : 



hence, the double meridian distance of a course is equal to 
the double meridian distance of the preceding course, plus the 
departure of that course, plus the departure of the course itself: 
if there is no preceding course, the iirst two terms become 
zero. We therefore have the following 

EuLE. — I. The double meridian distance of the first course 
is equal to its departure: 

II. The double meridian distance of the second course is 
equal to the double meridian distance of the first course, 2jIus its 
departure, plus the departure of the second course : 

III. The double meridian distance of any course is equal to 
the double meridian distance of the preceding course, plus its 
departure, jjIus the departure of the course itself. 

XoTE. — It should be recollected that ^^/^/-s is here used in 
its algebraic sense, and that, when the double meridian distance 
of a course, and the departure which is to be added to it, 
are of different names, that is, one east and the other west, 
they will haA'e contrary algebraic signs ; hence, their algebraic 
sum will be expressed by their numerical difference, with the 
si^n of the greater prefixed. 



SEC. m.] 



AEEA OF GROUND. 



131 



If the assumed meridian cuts the enclosure, the double 
meridian distances, estimated to the east are plus, and those 
on the west, must be taken with the minus sign. 

The double meridian distance of the last course should be 
equal to the departure of that course. A yerification of the 
work is therefore obtained, by comparing this double meridian 
distance with the departure. 



Area. 

97. Let us re&ume the example 
of Art. 75. We will first write the 
differences of latitude and the double 
meridian distances of the courses, 



in the following table. 




stations. 


Dif. of Latitude. 


D. M. D. 


Area. 

+ 


1 

Area. 


1 


+ cB 


+ Ua 


'ZcAB 




2* 


+ Bs 


+ ^P 


2BsC 




3 


-yD 


+ 2/i7i 




2visCD 


4 


-Df 


+ 'Zed 




2cmDA 



It is evident, that cB multiplied by 2I)a = cA, will giye 
double the area of the triangle cAB. But cB and ba are both 
plus; hence, the product will be pjlus, and must be put in 
the column of plus areas. Double the area of the triangle 
BsC, is equal to Bs multiplied by 2qp, which product is also 
plus. 

The area of the trapezoid 7ns CD is equal to yD = ms multi- 
plied by nil (Geom., Bk. IV., Prop. VII., S.) ; hence, double 



132 



ELEMENTS OF SURVEYING. 



[book II. 



the area is equal to yD into '^nli. But since yD (being a south- 
ing) is minus, and 2nli plus, it follows that the product will be 
negative; hence, it must be placed in the column of negative 
areas. 

Double the area of the trapezoid cADm, is equal to Df=mc 
multiplied by 2de : but, since Df is negative and 2cle positive, 
the product will be negative. 

It is now evident that the difference between the two columns 
is equal to twice the contents of the figure ABCD: and since 
the same may be shown for any other figure, we have, for finding 
the areas, the following general 

Rule. — I. Multiply the double meridian distance of each 
course ly its oiorthing or soutliing, observing that like signs in 
the multiplicand and multiplier give plus in the product, and 
that unlihe signs give minus in the product. 

II. Place all the products ivhich have a plus sign, in one col- 
umn, and all the prodMcts which have a minus sign, in another. 

III. Add up the columns separately and tahe the difference of 
their sums: this difference will be double the area of the land. 

98. We will now make the calculations of this example, in 
numbers, from the field-notes, which are the following: 



stations. 


Bearings. 


Distances. 


Dif. Lat. 


Dep. 


V). M. D. 


1 


N 31i° W 


10.40 


+ 8.86 


-5.44 


+ 1S.02 

— 7.14 

— 5.44 


+ 5.44 


2* 


N 62° E 


9.20 


+ 4.31 


+ 8.12 


+ 8.12 


3 


S 36° E 


7.60 


-6.15 


+ 4.46 


+ 8.12 
+4.46 


+ 20.70 


4 


,S 45rW 


10. 


-7.02 


-7.14 


4.46 
—7.14 


+ 18.02 



SEC. m.] 



AREA OF GROUND. 



133 



We see, from inspecting the notes, that 2 is the most westerly, 
and 4 the most easterly station. Either of them may, therefore, 
be taken for the principal station. Let us assume 2 for the 
principal station, through which, the assumed meridian passes, 
and distinguish it by a star, thus *. 

Having done so, we enter the departure 8.18 in the column 
of double meridian distances, which is the double meridian 
distance of the course from B to C. The double meridian 
distances of the other courses are calculated according to the 
rule; and as the last, which is that of the course from A to 
B, is equal to the departure of that course, the work is known 
to be right. 

Let us now form a new table, which will complete the 
arithmetical part of the work. 



sta. 


Bearings. 


Dist. 


Dif. Lat. 


D. M. D. 


Area. j Area. 

i 


1 


N 31i° W 


10.40 


+ 8.86 


+ 5.44 


48.1984 




2 


:N"62° e 


9.20 


+ 4.31 


+ 8.12 


34.9972 




3 


S 36° E 


7.60 


-6.15 


+ 20.70 




127.3050 


4 


S 45rW 


10. 


-7.02 


+ 18.02 




126.50041 












83.1956 


253.8054 



Area in sq. ch. 
Dividino: bv 10 



83.1956 

2)170.6098 
. 85.3049 
8.53049 
4 

2.12196 
40 



Ans. SA. 2E. 4.88 P. 



4.87840 



134 



ELEMENTS OF SURVEYING. 



[book n. 




Plotting. 

99. It now only remains to make 
a plot of the ground. 

For this purpose, draw any line, as 
NS, to represent the meridian passing 
through the principal station; and on 
this line take any point, as J?, to repre- 
sent that station. 



FIRST METHOD. 

' Having fixed upon the scale on which the plot is to be 
made, lay ofi" from B, on the meridian, a distance JBs equal to 
the difference of latitude of the second course, and at s erect 
a perpendicular to the meridian, and make it equal to the 
departure of that course: then draw BC, which will be the 
second course. 

Through C draw a meridian, and make Cf equal to the 
difference of latitude of the third course, and through / draw 
a perpendicular f^, and make it equal to the departure of that 
course: draw CD, and it will be the third course. 

Lay down, in the same manner, the courses DA and AB, 
and the entire plot will be completed. 



SECOND METHOD. 

The work may be plotted in another manner, thus. At 
the principal station B, lay off an angle equal to the bearing 
from B to C, which will give the direction oi BC. Then, from 
the scale of equal parts, make BC equal to the second course: 
this will give the station C. 

Through C draw a meridian, and lay off an angle equal to 
the bearing from C to D, and then lay off the course CD. Do 



SEC. III. 



AEEA OF GROUND. 



135 



the same for the bearing at D and the course DA ; also, for 
the bearing at A and' the course AB, and a complete plot of 
the ground will thus be obtained. If the work is all right, 
the first line AB, that was run, and the last line plotted, will 
exactly close the figure. This plot is made on a scale of 10 
chains to an inch. 



By Table oe Natural Sines. 

100. If the land surveyed be very valuable, and very great 
accuracy is necessary in the computation of the area, it may 
be w^ell to calculate it by means of the Table of Natural Sines 
(Bk. I., Art. 57). 

In this Table the degrees are marked at the top and bottom 
of each page, and the minutes at the left and right. The table 
being calculated to the radius 1, the sines and cosines are 
expressed in decimals of 1. When the Table is used for the com- 
putation of areas, the cosines are the differences of latitude, and 
the sines the differences of departure, to the distance 1. Hence, 
if the cosine and sine be taken from the table, for any course, 
and then multiplied respectively by the length of the course, 
the products will be the latitudes and departures for that 
course and distance. 

Let us resume the last example. 



stations. 


Bearings, 


Distances. 


LATITUDE. 


DEPARTURE. 


N 
+ 


s 


E 

+ 


w 


1 

2 
3 

4 


N 3ir W 
N62° E 
S 36° E 
S 45i° W 


10.40 

9.20 
7.60 
10. 


8.8675 
4.3191 


6.1486 
7.0091 


8.1231 

4.4672 


5.4340 
7.1325 



"We first take from the Table of Natural Sines, page 69 (of 
Tables), the cosine and sine of 31 T? which are .85264 and .5225. 



136 



ELEMENTS OF SURVEYING. 



[book II. 



We then multiply them by the distance 10.40, and the products 
8.867456 and 5.43400 are the latitudes and departures of the 
course ; which we enter in the table, omitting the decimals after 
the fourth place. We find, in a similar manner, the latitudes and 
departures of the other courses ; after which the work is balanced 
and wrought, as with the Traverse Table. 



EXAMPLEI 



1. It is required to determine the contents and plot of a 
piece of land, of which the following are the field-notes — viz. : 



sta- 
tions. 


Bearings. 


Dist. 


.Dif. 


■ Lat. 


Dep. 


BALANCKD. 


D.M.D. 

+ 


AREA. 

+ 


AREA. 


N 

+ 


S 


E 

+ 


W 


Lat. 


Dep. 


1 


N 46^0 W 


20.76 


14.29 






15.06 


+ 14.30 


-15.04 


15.04 


215.0720 




2 


N 51|o E 


13.80 


8.54 




10.84 




+ 8.55 


+ 10.86 


10.86 


92.8530 




3 


E 


21.35 






21.35 






+ 21.37 


43.09 






4 


S56o E 


27.60 




15.44 


22.88 




-15.43 


+ 22.90 


87.36 




1347.9648 


5 


s 3310 W 


18.80 




15.72 




10.31 


—15.71 


—10.29 


99.97 




1570.5287 


6 


N 74^0 W 


30.95 


8.27 






29.83 


+ 8.29 


—29.80 


59.88 


496.406-2 








E 


31.10 
rror.... 


31.16 

31.10 

.06 


55.07 


55.20 

55.07 

.13 


Error. 

An 


s. 105 A 


. 2i?. 


S04.3312 2918.4935 

804,3312 

2)2114.1623 

33 P. 1057.08115 



Plot of the ground. 




Note. — When the bearing is due East or due West, the error 
in latitude is . nothins:, and the corrections for latitude must 



SEC. III.] 



AREA OF GROUND. 



137 



be distributed among the other courses. So, when the- bearing 
is due North or due South, the error in departure is nothing, 
and the error in departure must be distributed among the 
other courses. In the examples for practice, we have not been 
as careful to have as close balances as must be had, in actual 
work on the field. 

2. Eequired the contents and plot of a piece of land, of 
which the following are the field-notes. 



stations. 


Bearings. 


Distances. 


i 


S 34° W 


3.95 ch. 


2 


S 


4.60 


3 


S 36i° E 


8.14 


4 


N 59^ E 


3.72 


5 


]^^ 25° E 


6.24 


6 


N 16° W 


3.50 


< 


N 65° W 


8.20 



Ans. 10 A. OE. 6 P. 

3. Eequired the contents and plot of a piece of land, from 
the following field-notes. 



stations. 


Bearings. 


Distances. 


1 


S 40° W 


70 rods. 


2 


N 45° W 


89 


3 


N 36° E 


125 


4 


.N" 


54 


5 


S 81° E 


186 


6 


S 8° W 


137 


7. 


W 


130 



Ans. 207 A. 3 E. 33 P. 



138 



ELB2JXXTS OF SUEYEYING. 



[book n. 



4. Required the contents and plot of a piece of land, from 



the following notes. 



Stations. 


Bearings. 


Distances. 


1 


S 40^° E 


31.80 ch. 


2 


:N^ 54° E 


2.08 


3 


N 29^ E 


2.21 


4 


]S^ 28r E 


35.35 


5 


X or w 


21.10 


6 


S 47^ W 


31.30 



Ans. 92 A. 3 i?. 32 P. 

5. Eeqnired the area of a suryey, of which the following 

are the field-notes. 



Stations. 


Bearings. 


Distances. 


1 


X 42^ E 


5.00 ch. 





East. 


400 


3 


X 9= E 


4.00 


4 


S 69^ E 


5.56 


5 


S 36^ E 


T.OO 


6 


S 42° W 


4.00 


.■v 


S 75° W 


10.00 


8 


S 39° W 


7.50 



If, in this example, we assume 1 as the principal station, 
the double meridian distances will all be plus, and the posi- 
tive area will exceed the negative. 

In balancing, we shall find the error in southing to be 
.28 ch., and in westing .22 ch. The area is 13 A. B. 11 P. It 
should, however, be remarked, that in all the examples the 
answers may be slightly varied by distributing the corrections. 



SEC. III.] 



AREA OF GEOUND. 



139 



6. What is the area of a survey of which the following 
are the field-notes ? Make the plot. 



stations. 


Bearings, 


Distances, 


1 


N 75° 00' E 


54.8 rods. 


2 


N 20° 30' E 


41.2 


3 


East. 


64.8 


4 


S 33° 30' W 


141.2 


5 


S 76° 00' W 


64.0 


6 


Xorth. 


36.0 


7 


S 84° 00' W 


46.4 


8 


N 53° 15' W 


46.4 


9 


N 36° 45' E 


76.8 


10 


K 22° 30' E 


56.0 


11 


S 76° 45' E 


48.0 


12 


S 15° 00' W 


43.4 


13 


S 16° 45' W 


40.5 



In this survey 4 is the most easterly and 9 tire most westerly 
station. The area is equal to 110^. 2i?. 23 P. It may vary a 
little, on account of the way in which the balancing is done. 

7. What is the area of a survey of which the following 
are the notes? Make the plot. 



stations. 


Bearings. 


Distances. 


1 


S 46i°. E 


80 rods. 


2 


S 51f° W 


55.20 


3 


West. 


• 85 


4 


N 56° W 


110.40 


5 


N 33i° E 


75.20 


6 


S 74i° E 


123.80 



A71S. 104: A. IB. 16 P. 



140 



ELEMENTS OF SURVEYING. 



[book n. 



8. Eequired the area of the farm, of which the survey- 
notes are given on page 117. 



stations. 


Bearings. 


Distances. 


A 


N 68° 55' 


W 


31.95 


B 


N 8° 


E 


1.40 


C 


S 87° 05' 


W 


22.89 


D 


N 30° 35' 


E 


8.39 


E 


N 43° 05' 


E 


23.91 


F 


N 87° 05' 


E 


14.51 


G 


S 64° 30' 


E 


7.55 


H 


S 71° 


E 


12.21 


I 


S 27° 


E 


17.39 


K 


S 30° 


W 


16.97 



Offsets between C and 
D to be added, 

15.9450 chains. 

Offsets to be subtract- 
ed, 15.1885 chains. 



Problems. 

I. To determine the bearing and distance from one point to another, 
when they are so situated that one cannot be seen from the 
other. 

101. Let A and (7 be the two points, 
and AB a meridian passing through 
one of them. From either of them, as 
A, measure a course A 2, of a con- 
venient length in the direction toward 
C, and take the bearing with the com- 
pass. At 2, take the bearing of a second 
course, and measure the distance to 3. 
At 3, take a third bearing and measure 
to 4. At 4, take the bearing to C, and 
measure the distance from 4 to C. 

Then, the dir-^ence between the sum of the northings and 




SEC. III.] 



AREA OF GROUND. 



141 



the sum of the southings will be denoted by AB ; and the 
difference between the sum of the eastings and the sum of the 
yrestings, by BC. The base AB, and the perpendicular BC oi 
the right-angled triangle ABC, are then known. The angle 
at the base, BAC, is the bearing from A to 0; or the equal 
alternate angle at C is the bearing from C to A, and the 
hypothenuse AC,- is the distance. 

Haying measured the bearings and courses on the field, 
form a table, and find the base and perpendicular of the right- 
angled triangle, in numbers ; after which, find the bearing and 
distance. 



Stations. 


Bearings . 


Distances. 


N. 


s. 


E. 


w. 




1 


N 61° W 


40 ch. 


19.39 






34.98 




2 


N 42° W 


41. 


30.47 






27.43 




3 


N 12° E 


16.10 


15.75 




3.35 






4 


N 47° E 


32.50 


22.16 




23.77 










AB-- 


= 87.77 




27.12 


62.41 












27.12 


ch. 




CB = 


= 35.29 



To find the angle BAC, or the bearing from A to C. 

Eadius : tan A : : AB : BC, 

or, AB : BC :: B : tan A; 

that is, applying logarithms, 

(a. c.) log AB (87.77) 8.056654 

log BC (35.29) 1.547652 

log i? 10. 

log tan A 21° 54' 12" 9.604306 



142 



ELEMENTS OF SURVEYING. 



[book n. 



To find the distance AC 

sm A : R :: BO : AC; 
Applying logarithms, 

(a. c.) log sin A 21° 54' 12 0.428242 

log 72 10. 

log BO (35.29) 1.547652 

log AC 94.6 1.975894 

Hence, the bearing and distance are both found. 

Note 1. — Had any of the courses run south, AB would have 
been equal to the sum of the northings, minus the sum of 
the southings. 

XoTE 2. — The last problem affords an easy method of finding 
the bearing and length of one of the courses of a survey, when 
the bearings and lengths of all the others are known. It may 
be necessary to use this method when there are obstacles which 
prevent the measuring of a course, or when the bearing cannot 
be taken. Indeed, tivo omissions may in general be supplied by 
calculation. It is far better, however, if possible, to take all the 
notes on the field. For, when any of them are supplied by 
calculation, there are no tests by which the accuracy of the 
work can be ascertained, and all the errors of the notes affect 
also the parts which are supplied. 

EXAMPLES. 

1. In a survey w^e have the following notes: 



stations. 


Bearings. 


Distances. 


1 

2 
3 
4 


N 314° W 
:N" 62f° E 

Lost. 
S 45i°W 


10 ch. 
9.25 

Lost. 
10.40 



SEC. in.] AEEA OF GROUND. 

What is the bearing distance from station 3 to 4 ? 



143 



(Bearing, S 38° 52' E. 
Ans. } 

(Distance, 7.03 ch. 



2. In a survey we have the following notes : 



stations. 


Bearings. 


Distances. 


1 


s m° E 


* 3L80 ch. 


2 


ISr 54° E 


2.08 


3 


Lost. 


Lost. 


4 


N 281° E 


35.35 


5 


N 57° W 


2L10 


6 


S 47° W 


3L30 



What is the bearing and distance from 3 to 4 ? 



A71S. 



Bearing, N 34° 47' E. 



Distance, 



2.19 ch. 



n. To determine the angle included between any two courses, 
when their bearings are known. 



102. Let NS be a meridian 
passing through A. 



Let AB, AC, AH, AD, and 
AF, be five courses running 
from A. We readily deduce the 



following 



AG isN 26° W 
AH is N 65° W 

(Lli?=39° 




Principles. 

When the meridional letters are alike, 
and those of departure also alike, the differ- 
ence of the leavings is the angle between 
the courses. 



lU 



ELEMENTS OF SURVEYrN'G. 



[book II. 



AB is N 46° E 

AC is ]sr 26° ^y 



CAB = 72° 

AC is N 26° W 
AD is S 66° W 



CAD = 180° - 92° = 88^ 



AC is N" 26° W 
AF is S 66^ E 



CAF= 180°-40° = U0° 



■^ When tlie meridional letters 
I are alike, and those of departure 
unlike, the sum of the hearings iS 
the angle between the courses. 

When the meridional letters 

are unlike, and those of departure 

J^ alike, the angle letween the courses 



is equal to 180°, minus the sum 
of the hearings. 

When the meridional letters 

are unlike, and those of departure 

> also unlike, the angle hetween the 

courses is ec[ual to the difference 

of the hearings taken from 180°. 



!N"oTE. — The above principles are deduced, under the sup- 
position that the two courses are both run from the same 
angular point. Hence, if it be required to apply these rules to 
two courses run in the ordinary way, as we go around the field, 
the bearing of one of them must be reversed before the calcu- 
lation for the angle is made. 



EXA3IPLES. 

1. The bearings of two courses, from the same point, are 
K 37° E, and S 85° W: what is the angle included between 
them? Ans. 132°. 

2. The bearings of two adjacent courses, in going round a 
piece of land, are X 39° W, and S 48° W: what is the angle 



included between them ? 



Ans. 87 



3. The bearings of two adjacent courses, in going round a 
piece of land, are S 85° W, and X 69° W : what is the angle 
included between them? Ans. 154°. 



SEC. III.] OF DIVIDING LAND. 145 

4. The bearings of two adjacent courses, in going ronnd a 
piece of land, are N" 55° 30' E, and S 69° 20' E : what is the 
angle included between them ? Aiis. 124° 50'. 

Latin^g out and dividing Land. 

103. The surveyor is often required to lay off a given 
quantity of land, in such a way that its bounding lines shall 
form a particular figure, viz., a square, a rectangle, a triangle, 
&c. He is also often called upon to divide given pieces of 
land into parts containing giyen areas, or, into areas bearing 
certain relations to each other. 

The manner of making such divisions must always depend, 
on a skilful and judicious application of the principles of 
geometry and trigonometry to the particular case. 

For example, if it were required to lay out an acre of 
ground, in a square form, it would be necessary to find, by 
calculation, the side of such a square, and then trace, on the 
ground, a figure bounded by four equal sides, at right angles 
to each other. 

PROBLEM I. 
104. To lay out a given quantity of land in a square form. 

Rule. — Reduce tlie^ given area to square chains, or square 
rods: tlien extract ilie square root, and the result will he the 
side of tlie required square. This square leing described on the 
ground, luill te the figure required. 

1. To trace a square which shall contain 15^. OR. 12 P.. 
First, 15 ^1 = 60 i^ = 2400 P ; hence, 

Add, 12 P 

15^ OP 12P=: 2412 P; the square root 
of which is 49.11, nearly. Therefore, if a square be traced on 
the ground, of which the side is 49.11 rods, it will be the 

required figure. 

10 



146 ELEMENTS OF SUEYEYIXG. [BOOK II. 

2. To trace a square which shall contain 176.4. 1 H. 24: F. 

First, 176^1 = 17G0 square chains, 

IE = 2.5 " " 

hence, 24P == 1.5 " " 



17G^ 1^= 24:. P = 176-1 square chains: the square 
root of which is 42. Hence, if a square he traced on the 
ground, of which the side is 42 chains, 'it will be the required 



figure. 



PEOBLE^I II. 

105. To lay out a given quantity of land in a rectangular form, 
when one of the sides of the rectangle is given. 

EuLE. — Divide the given area, reduced to square chains or 
scjuare rods, ly the given side of the reciuired rectangle, and 
the quotient will le the other side. Then, trace the rectangle 
on the ground. 

1. To lay off 240 acres in a rectangular form, one of the 
sides being given, and equal to 80 rods. 

. First, 240 A = 2400 square chains — 38400 square rods. 

Then, 80)38400(480 rods; which is the required side of the 
rectangle. 

1N"0TE. — A great number of similar problems might be pro- 
posed. The solution of them does not, however, properly belong 
to surveying. The laying out of the ground, and tracing of 
lines, after the figure and area have been determined, are the 
only parts which really appertain to a practical treatise. The 
manner of tracing lines having been already explained, it seems 
unnecessary to add the numerous examples often given under 
this head of the subject. 



SEC. III.] 



OF DIVIDING LAND. 



147 



PROBLEM IIL 

106. To run a line from the vertex of a triangular field which 
shall divide it into two parts, having to each other the ratio 

of m to 11. 



Let ABC be any triangular field. 

Diyide the side BC into two parts, 
sucli that (Geom., Bk. IV., Prob. I.) 

BD : DC :: m : n; 
and draAV the line AD : 
then will, ABD : DAC : : m 




n. 



For, the two triangles ABD, ADC having the same alti- 
tude, are to each other as their bases (Geom., Bk. IV., P. 6, 0.) : 
hence, the triangle is divided into parts having the ratio of 
m to n. 



PROBLEM IV. 

107. To run a line parallel to one side of a triangular field, that 
shall form with the parts of the two other sides a triangle 
equal to the — part of the field. 

Let CBA represent a triangular field, and CA the side 
parallel to which the dividing line is to be drawn. 

On the side BC describe a ^' -'-.^ 

semicircle: then divide BC at 
D, so that 

BD : BC w m : n. 

At D, erect the perpendicular 
DC to the diameter BC, and draw BC Then, with B as a 
centre, and BG as Sb radius, describe the arc of a circle 
cutting BC at E. Through E draw EF parallel to CA, and 
it will divide the triangle in the required ratio. For. (Geom., 
Bk. IV., P. 23), 



a.i' 




148 ELEMENTS OF SURVEYING. [BOOK 11. 

'BG' = ^^ = BCxBD; or, BE'' ^BC^X-^; whence, 

BE^ : BG^ :: BD : BC : m : n. 
But, since the triangles BEF, BOA are similar, 
BE^ : BC^ :: BEF : BOA. 
Wherefore, from equality of ratios, 

BEF : BCA :: m : n; 



whence, BEF =- X BCA. 

n 



I^OTE 1. — The points E and F may easily be found by 
computation. 

For, since BE^ = BG^ = BCx BE, and BD = - XBG, 
we have, 'BE' = mrx~; or, BE^BC V —- 

I lYl 

In like manner, BF = BAy — . 

EXA3IPLE. 

Let it be required to divide the triangular 
field CAB, in which ^(7=9 ch., AB = 11 ch., 
and CB = 7 ch., into two such parts that ABE 
shall be one-fourth of the whole field. 



In this case, we have 
m = 1, n = 4, and 



|/Z^ = /I 1 




n '4 2 
hence, AE = 4: ch. 50 1., and AD = 6 ch. 50 1. 



SEC. m.] 



OF DIVIDING LAND. 



149 



peoble:m y. 

108. To run a Hne from a given point in the boundary of a piece 
of land, so as to cut off, on either side of the line, a given 
portion of the field. 

Make a complete survey of the field, by the rules already 
given. Let us take, as an example, the field whose area is 
computed at page 136. That field contains 105^. 2 E. S3 P., 
and the following is a plot of it. 

N 



W 



C G 


71 


D 




^\3 \ 

\ \ / 
' ' / 


1 

1 


"^X,^ 


^^ 



Let it now be required to run a line from station A^ in 
such a manner as to cut off, on the left, any part of the field ; 
say, 26.4 2R 31 P. 

It is seen, by examining the field, that the division line 
will probably terminate on the course CD. Therefore, draw a 
line from A to (7, which we will call the first closing line. 

The bearings and lengths of the courses AB, BC, are 
always known; and in the present example are found in the 
table on page 136 : hence, the bearing and distance from C to 
.1 can be calculated by Art. 101 : they are, in this example, 
Bearing, S 19° 28' E = Course, 23.22 ch. 

Having calculated the bearing and length of the closing 
line, find, by the general method, the area which it cuts off: 
that area, in the present case, is 

14.4 0/i 26 P. 



150 ELEMENTS OF SURVEYIKG. [BOOK H. 

It is now evident that the diyision line must fall on the 
right of the closing line AC, and must cut off an area ACH, 
equal to the difference between that already cut off, and the 
given area : that is, an area equal 

26^ 2i? 31P given area, 

14.4 OR 26 P area already cut off, 

to ... . 12^1 2E 6F. \ 



Since the bearing of the next course CD, and the bearing 
of the closing line AC are both known, the angle A CD which 
they form with each other, can be calculated, and is in this 
example, 79° 32'. Hence, knowing the hypothenuse AC, and 
the angle ACC at the base, the length AG, the perpendicular 
let fall on the course CD can be found, and is 22.82 chains. 

Since the area of a triangle is equal to its base multiplied 
by half its altitude, it follows, that the base is equal to the 
area divided by half the altitude. Therefore, if the area 
12 A 2R dP 

be reduced to square chains, and divided by 11.41 chains, which 
is half the perpendicular AG, the quotient, which is 10.95 
chains, will be the base CH. Hence, if we lay off from C, on 
CD, a distance CR, equal to 10.95 chains, and then run the 
line AH, it will cut off, from the land, the required area, viz., 
26.4 2R 31 P. 
Note 1. — If the part cut off by the first closing line 
should exceed the given area, the division line will fall on the 

left of ^a 

Note 2. — If the difference between the given area and the 
first area cut off, divided by half the perpendicular AG, gives 
a quotient larger than the course CD; then, draw a line from 
A to D, and consider it as the first closing line, and let fall 
a perpendicular on DK 



SEC. III.] OF DIVIDING LAND. 151 

Note 3. — When the point from which the division line is 
to be draAvn falls between the extremities of a course, divide 
the course into two parts, at this point. Then consider one 
of the parts as an entire course, and the other as forming a 
new course, having the same bearing. The manner of making 
the calculation will then be the same as before. 



PKOBLEM VI. - 

109. To cut off from a field, a given area, by a line running in a 
given direction. 

In this case, as in the previous one, a complete and correct 
survey is first necessary. Then, w^hen the whole area is known, 
the position of the line may be approximately determined by 
the inspection of a correct map of the whole. 

We will take, for illustration, Example 4, page 138, of which 
the plot is on the next page. 

Let it be required to cut off from this area, 50 acres, by a 
line whose bearing shall be S 60° E, or K 60° W. 

We will make a trial of a line starting at 25 chains from 
station 6, on the 6th course. We will call this station A, 
and the trial line AB. 

In order to determine if the area cut off is equal to the 
required area, we must first determine the length of ^^ and 
of Bo. These cannot be determined by the method of sup- 
plying lost notes. 

We must first calculate the length of a line, starting at the 
proposed point, and running to the station nearest to the other 
extremity of the closing line. In this example, from A to 5. 
This is easily found to be 36.406 chains, and its bearing 
K 81° 13' E. 



152 



ELEMENTS OF SURVEYING. 



[book II. 



Now, in the triangle AJ3 5 we have one side and the 
angles, to find the remaining parts. AB is found to be 28.88 

6 




chains and B 6 to be 22.81 chains. We haye now the com- 
plete field-notes of the area cnt off. 



The area is found 
to be 58.5029 acres. 



It now remains to move this line northerly, so that the 
area contained between its present position and the new one 
shall be equal to 8.5029 acres. 



A 


S 60° E 


28.88 ch. 


B 


N 28rE 


22.81 


5 


N 57V W 


21.10 


6 


S 47° W 


25.00 



SEC. m.] 



PUBLIC LANDS. 



153 



Suppose the lines A 6 and ^ 5 be prolonged till tliey meet 
at some point, as V. 

Calculate A V and B V, also the area 
ABV. AV is found to be 92.19 chains 
and BV 88.18 chains. The area of 
the triangle ABV, is 127.29 acres. Let 
M2i represent the line sought. Then, 
we have two similar triangles, with all 
the sides of the one, and the areas of 
each, known ; for, FJ/LY must contain 
8.5029 acres less than AVB. Then, 
AM and BX are easily determined. '^ 

The complete notes of the area to be cut off, are 




:m 


S 60° E 


27.89 j 


N 


X 28r E 


19.82 


5 


X b:' w 


21.10 


6 


S 47^ ^ 


21.87. 



XoTE. — Fields are so Tariously shaped that it is difficnlt 
to give rules that will apply to all cases. It is by practice 
alone that facility is obtained in that branch of snryeying 
relating to the division of estates. We have given only a 
few examples that may serve as general guides, in the appli- 
cation of the principles of Plane Geometry, to such cases as 
may arise. 

Public Lands. 

110. Soon after the organization of the present govern- 
ment, several of the States ceded to the United States large 
tracts of wild land, and these, together with the lands since 
acquired by treaty and purchase, constitute what is called 
the public lands, or public domain. Previous to the year 
1802, these lands were parcelled out without reference to any 



154 ELEMENTS OF SURVEYING. [BOOK II. 

general plan, in consequence of which the titles often con- 
flicted Avith each other, and in many cases, seyeral grants 
covered the same area. 

In tlie year 1802, the following method of surveying the 
public lands, was adopted by Colonel Jared Mansfield, then 
Surveyor-General of the Northwestern Territory. 

111. The country to be surveyed is first divided, by 
meridians, six miles distant from each other ; and. then 
again, by a system of east and west lines, also six miles 
from each other. The country is thus divided into equal 
squares, which are called toivnsliips. Hence, each township 
is a square, six miles on a side, and contains thirty-six square 
miles. 

112. For the purpose of illustration, we have obtained 
from the general land-office the accompanying map, which 
represents a considerable portion of the State of Arkansas. 

The principal meridian in this survey is called the 5th 
meridian, and passes through the point of junction of the 
White river with the Mississippi. The principal base-line, 
running east and west, intersects this meridian a little to 
the east of White river; and from the meridian and base- 
line, reckoned from this point of intersection, all the ranges 
of townships are laid off". 

For example, 1 j^orth, will apply to all the townships 
lying in the first row north of the base-line : 1 South, 
will apply to all the townships in the first row south of 
the base-line. Eange 1. East, will apply to all the tow]i- 
ships lying in the first row, east of the 5th meridian: and 
Eange 1 West, will apply to all lying in the first row to 
the Avest of it. The small figures designate the rows of 
townships, reckoned north and south from the base-line, 
and the ranges reckoned east and west from the 5th meri- 




S location of Zand Office 
T Bovndarg of LandTiistricts 
o + Zd72 ds ofjere d for Sd Je 



iM.^^\WV^tl%aH .S^.HM 



156 



ELEMENTS OF SUEYEYING. 



[book n. 



dian. Thus, township 1 Xorth, range 4 West, has its exact 
place designated, and may be immediately located. 

113. The principal meridians, and the principal base-lines 
are established by astronomical observation, and the lines of 
subdivision run with the compass. 

For convenience in making surveys, and for the purpose 
of designating particular localities, a state or large tract, is 
often divided into parts called "Districts." There are three 
such districts in the map before us, the Lawrence County 
District, the Arkansas District, and the Mississippi District, 
the boundaries of which are designated by the full dark 
lines. 

114. Each township is divided into equal squares, by me- 
ridians one mile apart, and by east and west lines at the 
same distance from each other. Hence, each township is 
divided into 36 square miles, each one of which is called 
a section. The sections of a township are numbered from 
1 to 36, beginning at the northeast angle, and each con- 
tains 640 acres. 

The diagram exhibits the 36 sections of a township. 













\ 


6 


5 


4 


3 


2 


1-^ 


7 


8 


9 


10 


11 


12 


18 


17 


16 


15 


14 


13 


19 


20 


21 


22 


23 


24 


30 


29 


28 


27 


26 


25 


31 


32 


33 


34 


35 


36 



To describe a section accurately, we say, section number 
5, in tovrnship number 4 north, in range 3d west of a 



SEC. III.] VARIATION OF THE NEEDLE. 157 

knoT\'ii meridian; the one, for example, drawn through the 
moutli of White river. The description fixes precisely the 
place of the section. Go to the 3d range of townships, west 
of the known meridian, find township number 4 north, in 
this range, and lastly, section number 5 of that township. 
The corners of the sections should be marked by permanent 
corner-posts, or by lines blazed on trees. 

115. The sections are divided into half sections, quarter 
sections, and even into eighths of sections. The following 
table shows the contents of a township, and its subdivisions: 

1 township = 36 sections = 23040 acres. 
1 section = 640 acres. 
■J- section = 320 acres. 
^ section =160 acres. 
■J section = 80 acres. 

VaEIATION of THE NeEDLE. 

116. The angle which the magnetic meridiaa makes with 
the true meridian, at any place on the surface of the earth, 
is called the variation of the needle at that place. 

The variation is east, when the northern end of the nee- 
dle, after settling to a state of rest, lies on the east of the 
true meridian; and west, when it lies on the west side of 
that meridian. 

117. The variation is different at different places, and 
even at the same place it does not remain constant for any 
length of time. The variation is ascertained by comparing 
the magnetic with the true meridian. 

118. If we suppose a line to be traced through those 
jwints, where the needle points directly north and south, such 
a line is called the line of no variation. 



158 



ELEMENTS OF SURVEYING. 



[BOOK II. 



By referring- to a map of the United States, sucli line 
is easily traced; for, in the year 1870, it passed, very nearly, 
through Ealeigh, in the State of North Carolina, Cleveland, 
in the State of Ohio, and crossed the Saut of St. Mary's at 
the lower end of Lake Superior. If a compass, at that time, 
had been placed anywhere on this line, the needle would have 
pointed due north and south : hence, this line was then the 
line of no variation. 

At all points on the surface of the earth, the north end 
of the needle inclines toward the U?ie of no valuation: hence, 
for all points east of this line, the variation is West; and for 
all points west of it, the variation is Fast. 

Places where the Variation is West. 



West. 

+ 


Latitude. 


Longitude 


Nearest Place. 


Latitude. 


Longitude 


Nearest Place. 


0° 


85- 00' 


78° 


10' 


Raleigh ± 


41° 


30' 


81° 45' 


Cleveland ± 


V 


36° 00' 


77" 


20' 


Plymouth + 


40° 


80' 


80° 00' 


Pittsburgh - 


2° 


37° 00' 


76° 


25' 


Richmond - 


42° 


00' 


80° 10' 


Erie - 


3° 


39° 00' 


76° 


40' 


Anapolis — 


40° 


40' 


78° 00' 


Harrisburgh — 


4° 


40° 00' 


76° 


25' 


Harrisburgh — 


48° 


20' 


79° 00' 


Buffalo ± 


5° 


40° 00' 


75° 


25' 


Wilmington — 


43° 


00' 


78° 00' 


Buffalo - 


6° 


40° 00' 


74° 


10' 


Trenton — 


48° 


00' 


77° 10' 


Oswego + 


7° 


41° 00' 


74° 


00' 


New York — 


48° 


00' 


76° 00' 


Oswego ± 


8° 


41° 20' 


73° 


00' 


New Haven + 


44° 


00' 


76° 00' 


Oswego — 


9° 


42° 10' 


73° 


00' 


Hartford - 


48° 


00' 


74° 00' 


Albany — 


10° 


42° 00' 


71° 


35' 


Providence ± 


44° 


00' 


74° 00' 




11° 


42° 00' 


70° 


25' 


Boston — 


44° 


00' 


78° 00' 


Montpelier ± 


12° 


44° 00' 


72° 


00' 


Montpelier ± 


45° 


40' 


74° 00' 


Montreal + 


13° 


44° 00' 


71° 


00' 


Portland + 


46° 


00' 


73° 30' 


Montreal + 


14° 


44° 10' 


70° 


00' 


Portland — 


46° 


20' 


73° 00' 




15° 


44° 20' 


69° 


00' 


Augusta — 


46° 


20' 


72° 00' 




16° 


45° 00' 


69° 


00' 




47° 


00' 


72° 00' 


Quebec + 


17° 


45° 00' 


68° 


00' 




47° 


00' 


71° 00' 


Quebec + 


18° 


45° 00' 


67° 


00' 


St. Andrews 


47° 


00' 


70° 00' 





SEC. III.] VARIATION OF THE NEEDLE. 159 

119. The table on the last page, and the ODe which follows, 
on tlie next, have been constructed from the magnetic chart 
accompanying the Annual Report of the Coast Survey of 1865, 
and all the magnectic meridians are calculated for the year 
ISTO. 

On that chart, we find the meridian of no variation. It 
passes through Ealeigh, in the state of Xorth Carolina (very 
nearly), and through Cleveland, in the state of Ohio. East 
of it, is marked the magnetic meridian of one degree : that 
is, the magnetic meridian, at any point of which, the variation 
is 1 degree west. Two points of this meridian are noted in 
the table : viz., the point whose latitude is 36° north, and 
longitude 77° 20' west ; and also the point whose latitude is 
40° 30', and Igjigitude 80°. Marking these two points, on a 
map of the United States, the magnetic meridian of one degree 
variation, west, may be drawn. And in a similar manner any 
magnetic meridian (of which two points are indicated by the 
table), may be drawn. 

To aid in the ready selection of any point, indicated in 
the table, the prominent place, nearest to it, is written in 
the adjoining column ; and when the place lies east of the 
point (and consequently the point icest of the place), the 
sign + is annexed; and the sign — , when the place lies 
west of the point, and the sign ±, when the meridian j)asses 
through, or very near tlie place. Thus, in the meridian of 
1° variation, Plymouth, in Xorth Carolina, is east of the first 
point, and Pittsburgh, west of the second. 



160 



ELEMENTS OF SURVEYING. 



[book II. 



Places where the Variation is East. 



East. 


Latitude. 


Longitude. 


Name of Place. 


Latitude. 


Longitude. 


Name of Place. 


0° 


35° 


00' 


7S° 


W 


Ealei;?h 


41° 


30' 


81° 


45' 


Cleveland 




1° 


34° 


00' 


79° 


10' 


Wilmington + 


41° 


00' 


88° 


00' 


Detroit + 




2° 


33° 


OO' 


80° 


10' 


Charleston + 


43° 


00' 


84° 


30' 


Lansing — 




4° 


33° 


00' 


86° 


30' 


Milledgeville + 


40° 


00' 


85° 


30' 


Indianapolis — 




6° 


31° 


00' 


87° 


OC 


Mobile — 


42° 


00' 


88° 


lO' 


Chicago + 




7° 


30° 


00' 


89° 


20' 


New Orleans — 


43° 


00' 


89° 


25' 


Madison, In. + 




9° 


29° 


00' 


95° 


00' 


Galveston + 


38° 


00' 


91° 


20' 


St. Louis + 




13° 


32° 


00' 


115° 


00' 


San Diego — 


36° 


00' 


104° 


00' 


Santa Fe — 




16° 


. 37° 


15' 


122° 


00' 


San Francisco — 


40° 


20' 


112° 


00' 


Salt Lake City ■ 


- 


21° 


46° 


00' 


124° 


OO' 


Astoria + 















This table is interpreted like the preceding.- At San Diego, 
on the Pacific, the variation is 13° 25' East; at San Francisco, 
it is 16° 30'; and at the month of the Columbia riyer, it is 

21° 10' East. 



Methods of ascertai^^in^g the Vaeiatiok. 

120. The best practical method of determining the true 
meridian of a place, is by observing the north star. If this 
star were precisely at the point in which the axis of the 
earth, prolonged, pierces the heavens, then, the intersection of 
the vertical plane passing through it and the place, with the 
surface of the earth, would be the true meridian. But, the 
star being at a distance from the pole, equal to 1° 30' nearly, 
it performs a revolution about the pole in a circle, the polar 
distance of which is 1° 30', nearly. 

To the eye of an observer, this star is continually in 
motion, and is due north but twice in 24 hours; and is then 
said to be on the meridian. Now, when it departs from the 
meridian, it apparently moves east or west, for 12 hours, and 
then returns to the meridian again. When at its greatest 



SEC. m.] 



VARIATION OF THE NEEDLE. 



161 



distance from the meridian, east or west, it is said to be at 
its greatest eastern or western elongation. 

The following tables show the times of its greatest eastern 
and western elongations : 

Easteei^ Elongations. 



Days. 


April. 


May. 


June. 


July. 


August. 


Sept. 


1 


H. M, 

18 32 


H. M. 

16 35 


H. M. 

14 33 


H. M. 

12 35 


H. M. 

10 34 


H. M. 

8 32 


7 


18 09 


16 11 


14 09 


12 12 


10 10 


8 09 


13 


17 45 


15 47 


13 46 


11 48 


9 47 


7 45 


19 


17 22 


15 24 


13 22 


11 25 


9 23 


7 22 


25 


16 58 


15 00 


12 59 


11 01 


9 00 


6 58 



"Westekn" Elongations. 



Days. 


October. 


Nov. 


Dec. 


Jan. 


Feb. 


March. 




H. M. 


H. M. 


H. M. 


H. M. 


H. ai. 


H. M. 


1 


18 24 


16 22 


14 24 


12 21 


10 18 


8 28 


7 


18 01 


15 59 


14 00 


11 57 


9 55 


8 04 


13 


17 37 


15 35 


13 37 


11 33 


9 31 


7 41 


19 


17 13 


15 11 


13 13 


11 10 


9 07 


7 17 


25 


16 50 


14 48 


12 49 


10 46 


8 44 


6 53 



The eastern elongations are put down from the first of 

April to the first of October; and the western, from the first. 

of October to the first of April: the time is computed from 

12 at noon. The western elongations in the first case, and 

the eastern in the second, occurring in the daytime, cannot 

be used. Some of those put down are also invisible, occurring 

in the evening, before it is dark, or after daylight in the 

morning. In such case, if it be necessary to determine the 

11 



162 



ELEMENTS OF SURVEYING. 



[book II. 



meridian at that particular season of the year, let G hours 
be added to, or subtracted from, the time of greatest eastern 
or western elongation, and the observation be made at night, 
when the star is on the meridian. 

Azimuth Table. 



Years. 


Lat. 32° 
Azimuth. 


Lat. 34° 
Azimuth. 


Lat. 30° 
Azimuth. 


Lat. 3S° 
Azimuth. 


Lat. 40° 
Azimuth. 


Lat. 42° 
Azimuth. 


Lat. 44° 
Azimuth. 


1870 


1° 37f' 


1°40' 


1° 421' 


1° 451' 


1° 481' 


1° 511' 


1° 551' 


1871 


1° 37F 


1° 3^' 


1° 42' 


1° 44|' 


1° 47}' 


1° 51' 


1° 54|' 


1872 


1° 37' 


1° 391' 


1° 41f ' 


1° 441' 


1° 471' 


1° oOf 


1° 541' 


1873 


V 36V 


1° 38|' 


1° 411' 


1°44' 


1°47' 


1° 501' 


1° 53}' 


1874 


r 361' 


1° 381' 


1° 40J' 


1° 431' 


1° 461' 


1° 49|-' 


1° 531' 


1875 


1 oof 


1° 38' 


1° 401' 


1° 431' 


r 46' 


1° 491' 


1° 53' 


187G 


1° 35|' 


1° 37f' 


1° 40' 


1° 42|-' 


1° 45|' 


1° 49' 


1° 521' 


1877 


1°35' 


1° 371' 


1° 39i' 


1° 421' 


1° 451' 


1° 481' 


1° 52' 


1878 


1° 34J' 


1° 37' 


1° 391' 


1°42' 


1° 44|' 


1°48' 


1° 51}' 


1879 


1° 341' 


1° 361' 


1° 39' 


1° 411' 


1° 441' 


1° 47|' 


r 511' 


1880 


1° 34' 


1° 36' 


1° 381' 


1° 41' 


r 44' 


1° 471' 


r 50}' 



The above table exhibits the angle which the meridian 
plane makes with the vertical plane passing through the pole- 
star, when at its greatest eastern or western elongation ; such 
angle is called the azimuth. The mean angle only is put 
down, being calculated for tlie first of July of each year. The 
use of the above tables in finding the true meridian will soon 
appear. 

To FIND THE TRUE MERIDIAN WITH THE THEODOLITE. 

121. Take a board, of about one foot square, paste white 
paper upon it, and perforate it through the centre; the diam- 
eter of the hole being somewhat larger than the diameter of 



SEC. m.] VARIATION OF THE NEEDLE. 163 

the telescope of the theodolite. Let this board be so fixed to a 
vertical staff, as to slide np and down freely: and let a small 
piece of board, about three inches square, be nailed to the 
lower edge of it, for the purpose of holding a candle. 

About tTrenty-fiye minutes before the time of the greatest 
eastern or western elongation of the pole-star, as shown by the 
tables of elongations, let the theodolite be placed at a conyen- 
ient point and lerelled. Let the board be placed about one 
foot in front of the theodolite, a lamp or candle placed on the 
shelf at its lower edge ; and let the board be slipped up or 
down, until the pole-star can be seen through the hole. The 
light, reflected from the paper, will show the cross-hairs in the 
telescope of the theodolite. 

Then, let the vertical spider's line be brought exactly upon 
the pole-star, and, if it is an eastern elongation that is to be 
observed, and if the star has not yet reached the most east- 
erly point, it will move from the line toward the east, and the 
reverse when the elongation is west. 

At the time the star attains its greatest elongation, it will 
appear to coincide with the vertical spider's line for some 
time, and then leave it, in the direction contrary to its former 
motion. 

As the star moves toward the point of greatest elongation, 
the telescope must be continually directed to it, by means of 
the tangent-screw of the vernier plate; and when the star has 
attained its greatest elongation, great care should be taken that 
the instrument be not afterward moved. 

Xow, if it be not convenient to leave the instrument in 
its place until daylight, let a staff, with a candle or small 
lamp upon its upper extremity, be arranged at thirty or forty 
yards from the theodolite, and in the same vertical plane with 
the axis of the telescope. This is easily effected, by revolving 
the vertical limb about its horizontal axis, without moving 



164 ELEMENTS OF SURVEYING. [BOOK H. 

the yernier plate, and aligning the staff to coincide with the 
vertical hair. Then mark the point directly under the theodo- 
lite; the line passing through this point and the staff, makes 
an angle with the true meridian equal to the azimuth of the 
pole-star. 

From the table of azimuths, take the azimuth correspond- 
ing to the year and nearest latitude. If the observed elonga- 
tion was east, the true meridian lies on the west of the line 
which has been found, and makes with such line an angle 
equal to the azimuth. If the elongation was west, the true 
meridian lies on the east of the line found: and, in either 
case, laying off the azimuth angle with the theodolite, gives 
the true meridiau. 

To FIND THE TEUE MeEIDUN WITH THE COMPASS. 

122. 1. Drive two posts firmly into the ground, in a line 
nearly east and west ; the uppermost ends, after the posts are 
driven, being about three feet above the surface, and the posts 
about four feet apart: then lay a plank, or piece of timber 
three or four inches in width, and smooth on the upper side, 
upon the posts, and let it be pinned or nailed, to hold it firmly. 

2. Prepare a piece of board four or five inches square, and 
smooth on the under side. Let one of the compass-sights be 
placed at right angles to the upper surface of the board, and 
let a nail be driven through the board, so that it can be 
tacked to the timber resting on the posts. 

3. At about twelve feet from the stakes, and in the direc- 
tion of the pole-star, let a plumb be suspended from the top 
of an inclined stake or pole. The top of the pole should be 
of such a height that the pole-star will appear about six 
inches below it ; and the plumb should be swung in a vessel of 
water to prevent it from vibrating. 



SEC. m.] VAEIATION OF THE NEEDLE. 165 

This being done, about twenty minutes before the time of 
elongation, place the board, to which the compass-sight is 
fastened, on the horizontal plank, and slide it east or west, 
until the aperture of the compass-sight, the plumb-line, and 
tlie star, are brought into the same range. Then if the star 
depart from the plumb-line, move the compass-sight, east or 
west, along the timber, as the case may be, until the star shall 
attain its greatest elongation, when it will continue behind 
the plumb-line for several minutes; and will then recede from 
it in the direction contrary to its motion before it became 
stationary. Let the compass-sight be now fastened to the hor- 
izontal plank. During this observation it will be necessary to 
have the plumb-line lighted: this may be done by an assistant 
holding a candle near it. 

Let now a staff, with a candle or lamp upon it, be placed 
at a distance of thirty or forty yards from the plumb-line, and 
in the same direction with it and the compass-sight. The 
line so determined, makes, with^ the true meridian, an angle 
equal to the azimuth of the pole-star ; and, from this line, the 
variation of the needle is readily determined, even without tra- 
cing the true meridian on the ground. - 

Place the compass upon this line, turn the sights in the 
direction of it, and note the angle shown by the needle. !N"ow, 
if the elongation, at the time of observation, was west, and the 
north end of the needle is on the west side of the line, the 
azimuth, plus the angle shown by the needle, is the true varia- 
tion. But should the north end of the needle be found on the 
east side of the line, the elongation being west, the difference 
between the azimuth and the angle would show the variation: 
and the reverse when the elongation is east. 

Note. — The variation of the needle should always be noted 
on every survey made with the compass, and then if the land 



166 ele:iiexts of sueyeying. [book ii. 

be surYejed at a future time, the old lines can always be 
re-run. 

123. It lias been found by obserYation, that heat and 'cold 
sensibly affect the magnetic needle, and that the same needle 
will, at the same place, indicate different lines at different hours 
of the day. 

If the magnetic meridian be obserYed early in the morning, 
and again at different hours of the day, it will be found that 
the needle will continue to recede from the meridian as the day 
adYances, until about the time of tlie highest temperature, when 
it will begin to return, and at CYening will make the same line 
as in the morning. This change is called the diurnal variation, 
and Yaries, sometimes, during the summer season, from one-fifth 
to one-fourth of a degree. 

124. A Yery near approximation to a true meridian, and con- 
sequently to the Yariation, may be had, by remembering that 
the pole-star Yery nearly reaches the true meridian, when it is 
in the same Yertical plane with the star Alioth in the tail of 
the Great Bear, which lies nearest the four stars forming 
the quadrilateral. 

The Yertical position can be ascertained ^ 

by means of a plumb-line. To see the i 

spider's lines in the field of the telescope, I 

at the same time with the star, a faint' 1 

light should be placed near the object-glass. 
"When the plumb-line, the star Alioth, and 
the north star, fall on the Yertical spider's 
line, the horizontal limb is firmly clamped, 
and the telescope brought down to the '^ 
horizon; a light, seen through a small aper- i 

ture in a board, and held at some distance 
by an assistant, is then moYcd according to signals, until it is 



> 


it 


i 


/ \ 


> 


/ > 


i 


-■>f--. / 


~^'" 


V 



SEC. IV.] TEIANGULATION. 167 

covered by the intersection of the spider's lines. A picket 
driven into the ground, nnder the light, serves to mark the 
meridian line for reference by day, when the angle formed by it 
and the magnetic meridian may be measured. 



SECTION IV. 

TRIANGUL ATION. 



125. When a large extent of territor}^, or a long line of 

sea-coast is to be surveyed, it becomes necessary to consider 
the curvature of the earth's surface; this branch of surveying 
is called Geodesic surveying. 

126. The operations necessary to the successful execution 
of a Geodesic Survey, require the minutest attention, and when 
performed, numerous corrections are to be applied to the meas- 
ured lines and angles, on account of the various causes of error 
incident to such operations. 

To investigate those causes of error, and to deduce rules for 
correcting the errors, in all cases, would far exceed the limits 
of an elementary treatise. We shall, therefore, attempt nothing 
more than a brief outline of the operations in a trigonometrical 
survey, in which the Plane-Table and Compass are used in con- 
nection with the Theodolite, and in which, the curvature of the 
earth is not considered. We shall then explain the methods 
of mapping, or plotting, such a survey. The example will be 
limited to the survey of the harbor, delineated in plate 6. 

127. After having made a preliminary examination, or re- 
connaissance of the territory to be surveyed, suitable stations 
are selected at the most prominent points, and these points are 
marked by staves or signals. 



168 ELEMENTS OF SURVEYING. [BOOK II. 

A hase-line is then measured. The length of the base will, 
in general, depend upon the magnitude of the survey, and each 
extremity is marked by a signal. 

The next step is the triangulation. At each extremity of the 
base, the angles between the base, and the lines drawn to each 
of the visible signals, are carefully measured by means of a 
theodolite. The sides of the triangles, thus obtained, serve as 
new bases upon w^hicli other triangles may be formed, and so on, 
until the entire area is covered by a net-work of triangles. 

This system of triangles is called the primary system, and 
the operation of forming them is called the primary triangula- 
tion. Within the primary triangles, and depending upon them, 
a system of smaller triangles is formed in the same manner, 
called the secondary system; and if the extent or importance 
of the work should demand it, the secondary may be sub- 
divided into tertiary triangles. 

Having completed the triangulation, the characteristics of 
the surface, such as roads, streams, villages, boundaries, &c., 
are filled in by means of the compass, plane-table, or some of 
the methods already explained. 

128. Before commencing a trigonometrical survey, an ex- 
amination of the entire territory should be made, for the pur- 
pose of selecting a location for the base-line, and proper points 
for stations ; this examination should be more or less elaborate, 
according to the nature and extent of the survey. 

The proper distribution and combination of the triangles, 
so as to adapt them to the survey in hand, require gTeat judg- 
ment and care, and but few rules can be given for the selection 
of trigonometrical points. Those points should, in general, be 
chosen in such a manner, that they may be distinctly visible 
from each other, and so that the triangles formed, by uniting 
them, may be, as nearly as possible, equilateral. 



SEC. IV.] TRIANGULATION. 169 

It is easily seen, that a triangle which has an obtuse or a 
very acute angle, will experience a greater change of form, for a 
given error, than one wiiich is nearly equilateral ; and since the 
accuracy of each triangle depends upon the preceding ones, it is 
further evident, that the introduction of a single ill-conditioned 
triangle, might vitiate the whole survey. Except in extreme 
cases, no angle, less than 30°, should be used; and even angles 
of 30° should not be admitted when the locality can be so chosen 
as to prevent it. The base is usually much shorter than the 
sides of the primary triangles; these sides, however, should be 
increased as rapidly as is consistent with the above remarks. 

129. The stations are marked by signals, which may be con- 
structed in a great variety of ways, depending upon the locality 
of the stations, and the lengths of the sides of the triangles. 

Sometimes a signal has to be raised above the level of the 
adjacent country, in which case it is constructed of timbers, 
and upon the apex, is placed a vertical staff, bearing a flag. 
The exact trigonometrical point is determined by a plumb-line, 
suspended from the apex of the signal. 

A temporary signal may be constructed with 
three or four pieces of scantling framed and traced, 
as shown in the annexed figure, with a short pole 
projecting from the apex. The plumb determines 
the point B, which is the exact trigonometrical 
point over which the theodolite is to be placed. 
Where the sides of the triangles are not very great, 
a pole, planted vertically, and surmounted by a 
flag, will answer as a signal. 

In order to distinguish the different signals, the flags which 
they bear, should be different from each other. They may be 
formed by arranging stripes of white and red, according to 
some prearranged plan, and the flags of the different stations 




170 ELEMENTS OF SURVEYING. [BOOK II. 

should be entered in a book. For the purpose of future reference, 
the trigonometrical point, at each station, as B, should be indi- 
cated by a permanent mark. If the point falls upon a rock, a 
hole may be drilled to show the locality ; or if not, a mark-stone 
may be sunk under the point, deep enougli to be beyond the 
reach of accident. A record of the monument should be pre- 
served, together with its reference to some of the permanent 
objects in the neighborhood. 

130. The measurement of a base-line on which the accuracy 
of the entire survey depends, is one of the most difficult opera- 
tions of surveying, and one, for the successful accomplishment 
of which, art and science have been strongly taxed. The selec- 
tion of a proper site for a base-line, forms one of the first objects 
of the preliminary reconnaissance. It should, if possible, be 
fixed on an open plain. It must be so chosen, that the sur- 
rounding signals may be distinctly seen from its extreme points ; 
and hence, those signals which mark points of the adjacent 
triangulation, should be selected with reference to the base. 
The length of the liase, should, in a measure, depend upon the 
magnitude of the survey. 

Theodolite. 

131. The theodolite is generally used for measuring the 
angles of a trigonometric survey. The extent of the survey, 
and the standard of accuracy to which the results are required 
to conform, must determine the size and perfection of the in- 
strument to be employed. The angles of the primary triangles 
of the United States Coast Survey are measured with theodo- 
lites, whose horizontal circles are 24 or 30 inches in diameter; 
and to eliminate, as much as j^ossible, every source of error, 
great numbers of observations are made at each station, the 
readings being made on different points of the arc by difierent 



SEC. IV.] 



TRIANGULATION. 



171 



yerniers. Usually from 4:0 to 60 observations are made for 
each angle — one measurement, ^vitli the telescope cHrect, and 
one with it reverted, constituting a complete observation. AVitli 
these precautions, it has been found that the error in a primary 
triangle (where the sum of its three angles has been compared 
with 180°), has fallen much within 3 seconds. The error of 
3 seconds has been adopted as the highest admissible limit 
of error. 

132. To illustrate the manner of carrying on a minor 
triaugulation, let us refer to the plan of the harbor [plate 6], 
in which AB is the measured base, 11-40 yards ; C, D, E, &C;, 
triaugulation points, at which signals have been erected. Com- 
mence the triaugulation at A, the west end of the base ; and 
for convenience in plotting, it would be well to make the 
line, passing * through the point and 180° parallel, in each 
position of the instrument, to the base AB. Having brought 
the of the vernier to the of the limb, clamp the vernier 
plate, and direct the upper telescope to the signal at B, and 
clamp the limb. Enter the observations as in the following 
tahle : 

Obseryatioxs at Station A. 



Name of Station. 


Vernier I. 


Vernier II. 


Mean. 


Station B 


00° 00' 00" 


00' 00" 


00° 00' 00" 


Station E 


72° 21' 55" 


25' 5" 


72° 25' 00" 


Station Ct 


138° 31' 56" 


35' 4" 


138° 35' 00" 


&c. 


&c. 


&c. 


&c. 



Having recorded the reading of the first vernier, and the 
minutes and seconds of the second vernier, unclamp the vernier 
plate, and direct the telescope to the station at E, and record 
both verniers, as before. Again unclamp the vernier plate, 



172 ELEMENTS OF SURVEYING. [BOOK H. 

and direct the telescope on the signal at G ; and then read 
and record, as before. 

Having determined the angles subtended by all the signals 
visible from A, let the theodolite be removed to B. Bring 
the of the vernier one, to 180° on the limb, and direct 
the telescope on the signal at A — the line (0°, 180°) will then 
be parallel to its first position, and the limb may be clamped. 
Read, now, the angles to the signals at A, E, C, &c., and record 
as before. 

If the theodolite is how removed to the station E, the line 
(0°, 180), may be made parallel to its first position, by adding 
180° to the reading of the first vernier, from A to E, and 
then directing the telescope on the signal at A. The line 
(0°, 180°), will thus be made parallel to AB, and the readings 
may be made and recorded as before; and so on* until all the 
stations have been visited, and the angles measured. From 
the field records, the angles BAE, EAG, ABE, EBG, &c., may 
be easily deduced, the whole may be plotted on paper, or the 
several sides may be computed trigonometrically. It may be 
observed that the line (0°, 180°), has been made parallel to 
the lase-line at each station. 

133. To illustrate this principle of repetition, suppose the 
of the vernier to coincide with the of the limb, and the tele- 
scope to be directed, from the station A, upon one of the objects, 
as the signal at B. Clamp the limb, and unclamping the vernier 
plate, direct the telescope on the second object, as the signal 
at E. If we now clamp the vernier plate, and unclamping the 
limb, direct the telescope on the signal at B, the line (0°, 180°), 
of the limb, will make with AB, an angle equal to BAE. 
Again clamp the limb, and unclamping the vernier plate, direct 
the telescope on the signal at E. The reading will evidently be 
equal to twice the angle BAE ; and if we repeat the operation. 



SEC. IV.] 



TRIANGULATION. 



173 



the reading will be three times the angle, and so on. After 
fen repetitions, if we add 360° each time the of the vernier 
passes the of the limb, the final reading will be ten times the 
angle BAE, affected with the joint errors of the ten observations, 
and one-tenth of this will be the reading required, to a greater 
degree of accuracy than could probably be attained by a single 
observation. 

134. The method of reading angles, by this mode, is as 
follows : 

Angles at station A, between signals B (left), and E (right). 

June StJi, 1870. 



No. of Repe- 
titions. 


Vernier I. 


Vernier n. 


Mean of Verniers. 


/ 


1 


72° 24' 55" 


25' 5" 


72° 25' 00" 


2 


144° 49' 55" 


50' 0" 


144° 49' 58" 




3 


217° 14' 50" 


15' 10" 


217° 15' 00" 




4 


289° 39' 50" 


40' 00" 


289° 39' 55" 








Mean reading 


4)289° 39' 55" 






72° 24' 59" 



Having measured the necessary angles, the parts of all the 
triangles, formed by joining the stations, three and three, may 
be readily calculated by methods heretofore explained. 



riLLIN"G UP THE SUEVET. 

135. After the triangulation is completed, the interior may 
be filled up by the aid of the Compass, on the plane-table, or 
both. 

Use of the Compass. 

136. The use of the Compass, in determining points and 
lines, by means of offsets, has been already explained (Bk. II., 



174 



ELEMENTS OF SURVEYING. 



[book II. 



Art. 83). Wc will apply these principles, in the example 
before us. 

Place the compass at A (plate 6), and take the bearing of 
the line AF, which is S 12° W. 




Enter this bearing at A. Then measure along the line AE 
any distance, as Aa equal to 130 yards, and make an offset to 
the lake, which wo measure and find to be 50 yards. Enter 
the 130 in the middle column, and as the lake lies on the right 
(in going from A to E), we insert the 50 in the right-hand 
column. 

"We then measure along the line AB to h, 350 yards from A. 
Here we make a second offset to the lake, and find it to be equal 
to 100 yards. Haying entered the distances in the notes, we 
measure to q, the point where the line AE crosses the creek, 
and we enter the distance from A, 415 yards. 

At d, we lay off an offset on the left, to the pond, 70 yards ; 
at e, an offset to the mouth of the creek, 150 yards ; and at E, 
where tlie course terminates, an offset to the lake, of 160 yards. 
The entire distance from ^ to ^ is 800 yards. 



SEC. lY.] THE PLANE-TABLE. 175 

At E, we take the beariug to //, wliicli is N 50° E. Haying 
measured along this line to /, 315 yards, we make an offset to 
the pond, on the left, of 50 yards, and to the shore, on the right, 
of 90 yards. Having entered these distances, we recommence 
the notes at 315, below, which we suppose to be at the bottom 
of the second page. Having reached H, the extremity of the 
course, we enter the entire distance from E, 680 yards. We 
next take the bearing to /, S 52° E. We then measure the dis- 
tances to m, n, p, and /, and enter them, together with the 
offsets, as in the notes. 

It is also well to make, in the columns on the right and left, 
such sketches of the ground, fields, houses, creeks, and rivers, 
as will afford the means of making an accurate delineation on 
paper. 

The Plajte-Table. 

137. The plane-table (PL 3, Fig. 1) consists of two parts: 
a rectangular board CDBA, and a tripod EHG, to Avhich it 
is firmly secured. 

Directly under the rectangular board are four milled screws 
which pass through sockets inserted in a horizontal brass plate : 
these screws are worked against a second horizontal plate, for 
the purpose of levelling the table ; the table having a ball-and- 
socket motion, similar to the limb of the theodolite. 

For the purpose of levelling the table, a small detached 
spirit-level is used. This level being placed over the centre, 
and also over two of the levelling screws, the screws are 
turned contrary ways until the level is horizontal; after which, 
it is placed over the other two screAvs, and made horizontal i]i 
the same manner. 

Between the upper horizontal plate and the table, there is 
a clamp-screw, similar to the clamp-screw of the theodolite, 
which being loosened, the table can be turned freely about 



176 ELEMENTS OF SURVEYING. [BOOK II. 

its axis. There is, also, a small tangent-screw, by wliicli the 
smaller motions of the table are regulated, after the clamp- 
screw is made fast. Neither of these screws can be seen in 
the figure. 

The upper side of the table is bordered by four brass 
plates, about one inch in width, and the centre of the table 
is marked by a small pin, F. About this centre, and tangent 
to the sides of the table, conceiye a circle to be described. 
Suppose the circumference of the circle to be divided into 
degrees and parts of a degree, and radii to be drawn through 
the centre and the points of division. The points in which 
these radii intersect the outer edge of the brass border, are 
marked by lines on the brass plates, and the degrees are 
numbered in the direction from left to right, from the point 
L to the point /, 180°, and from the point / to the point X, 
180°. In some plane-tables, however, they are numbered from 
to 360°. 

There are, generally, diagonal scales of equal parts cut on 
the plates BLG and AIB, the use of which will be explained 
hereafter. 

Near the two other edges of the table, two small grooves 
are made, into which the plates of brass BB and CA are fitted, 
and these plates are drawn to their places by means of milled 
screws, which pass through the table from the under side, 
and screw firmly into the plates. The heads of two of the 
screws, Q and 8, are seen in the figure, as also one of the 
plates and its two screws in Fig. 3. The object of these plates 
is to confine a sheet of paper on the table. By loosening the 
screws, and pressing them upward, the plates are raised above 
the surface of the table; the edges of the paper can then be 
placed under them: then, by turning the screws back again, 
the plates are drawn down and the paper held tightly. Tig. 1 
represents the table with the paper partly put upon it: one 



SEC. IV.] THE PLANE-TABLE. 177 

edge of the paper has been placed under the plate DB, and 
the screws S and Q tightened. The paper, before being put 
on, should be moistened, in order to expand it; and then, 
after it has been dried, it will fit closely to the table. 

A ruler, AB (Fig. 2), with open vertical sights, is used with 
the plane-table. This ruler has a fiducial edge, which is in the 
same vertical plane with the hairs of the sights. A ruler with 
a telescope, and a vertical limb, similar to the vertical limb of 
the theodolite, is sometimes used with the plane-table. A com- 
pass, also, is often attached to the table, to show the bearings 
of the lines. 

Uses oe the Plake-Table. 

138. The plane-table is used for two distinct objects. 

1st. For the measurement of horizontal angles: and, 

t 
2dly. For the determination of the shorter lines of a survey,. 

both in extent and position. 

To MEASUKE A HOKIZOKTAL AkGLE. 

139. Place, by means of a plumb, the centre of the table- 
directly over the angular point : then level the table ; after • 
which, place the fiducial edge of the ruler against the small; 
pin at the centre: direct the sights to one of the objects, and. 
note the degrees on the brass plate; then turn the ruler and' 
sights to the other object, and note the degrees as before. If ' 
the ruler has not passed over the point, the difference of the 
readings is the angle sought; but, if it has, take the larger, 
sum from 180°, and to the remainder add the smaller^ their 
sum is the required angle. 

To DETEKMINE Lliq"ES 11^ EXTEi^T AKD POSITION". 

140. Having placed a paper on the table, examine the 
objects and lines which are to be determined, and; select, for a. 



178 ele:u:ents of suryeying. [book ir. 

base, such a line of the triangulation that most of the objects 
can be seen from its extremities. Then place the plane-table, 
with its centre, nearly, though not accurately, over one ex- 
tremity of the base ; make it truly horizontal, and turn it until 
the larger part of the paper lies on the same side of the base, 
with the objects. 

Then, tighten the clamp-screw, and mark with a pointed 
pin the point of the paper directly over the station, which point 
is determined most accurately by suspending a plumb from 
the lower side of the table. Press the pin firmly on this 
point, bring the fiducial edge of the ruler against it, and sight 
to the other extremity of the base-line, and mark, with the pin 
or pencil, the direction of the line on the ]3aper. Sight, in 
like manner, to every other object, and draw on the paper 
the corresponding lines, numbering them from the base-line, 
1, 2, 3, 4, &c. 

Then, with a jiniv of dividers, take from the scale a certain 
number of equal ^arts, to represent the base, and lay off the 
distance on the base-line from the place of the pin. Take up 
the table, carry it to the other extremity of the base, and 
place the point of tlie paper corresponding to that extremity, 
directly over it. Place the fiducial edge of the ruler on the 
base-line, and turn the table, by means of the tangent-screw, 
until the sights are directed to the first station. If, however, 
in bringing the table to this position, the corresponding point 
of the paper has been moved from over the extremity of the 
base-line, move the legs of the tripod until it is brought 
back to its place. Let the table be then levelled, after which, 
place the ruler again on the base-line, and bring the table 
to its proper position, by the tangent-screw, and continue the 
adjustment until the extremity of the base-line, on the paper, 
is directly over the station, and in the same vertical plane 
witli the base-line, on the ground. Then direct the sights to 



SEC. IV.] 



THE PLANE-TABLE. 



179 




all the objects sighted to, from the other station, and mark 
the lines 1, 2, 3, 4, &c., from the base-line, as before. The 
intersections of the corresponding lines 1,1, 2,2, 3,3, 4,4, &c., 
determine, on the paper, the positions of the several objects, 
and a reference of these lines to the scale of equal parts, 
determines the true distances. 

141. Let it be required, for 
example, to determine, by means 
of the plane-table, the relative 
positions of several houses. 

From station A, and on one 
of the lines of the triangulation, 
as AB, measure the base-line 
AJV, which we will suppose equal to 300 yards. Place the 
plane-table at A, and sight to the corners of the houses, and 
mark the lines 1, 2, 3, 4, &c. Then remove the table to JV, 
and sight to the same corners as before, and draw the lines 
as in the figure. The points at which they intersect the cor- 
responding lines, before drawn, determine the corners of the 
houses. The front lines of the houses may then be drawn on 
the paper. Draw lines at right angles to the front lines, and 
on them lay off the depths of the houses, with the same scale 
as that used for the base-line. 

To find the length of any line drawn on the paper, as the 
line 1, drawn through A, for example, place the dividers at A 
and extend them to the other extremity of the line, and then 
apply the line to the scale. The length of the line 1 is equal to 
198 yards. 

142. In this example, we de- 
termine from the base-line CD, 
the positions of the points I^, 
E, and // 

i 




180 



ELEMENTS OF SURVEYING. 



[book n. 



Changing the Paper. 

143. "When one paper is filled, and there is yet more work 
to be done, let the paper be removed, and a second paper put 
on the table ; after which, the table may be used as before. 

ISTow, in order that the two papers may be put together and 
form one entire plan, it is necessary that two points, determined 
on the first paper, be also determined on the second; and then, 
by placing the lines joining these points, one on the other, all 
the lines on the two papers will have the same relative position 
as the corresponding lines on the ground; and the same for as 
many papers as it may be necessary to use. If different scales 
are used, the corresponding points will not join, and then the 
work must be reduced to the same scale, before the papers can 
be put together. 

In the first example, the position of the point F was deter- 
mined, in order to unite the first paper with the second. 

In the second example, we sighted from C and D, the ex- 
tremities of the base-line, to the points N and F, determined 
on the first paper; we thus determined the line IsF on the 
second paper. Placing the line NF of the one paper on NF of 
the other, we have the folloY/ing plan. 




In this plan, all the points and lines are accurately laid 
down. Any number of papers may be joined in a similar 
manner. 



SEC. IT.] CIECULAR PEOTEACTOE. 181 

144. The principal use of the plane-table is for the interior 
filling up of trigonometrical surveys: it is also used with advan- 
tage, Tvhen only a plot of a field is wanted. 

It ought not be used for the determination of long lines, nor 
can it be relied on for determining extended areas. 

Plotting the Teiaxgulatiox. 

145. The sides of the triangles having been completed, the 
work may then be plotted, as already explained, either by means 
of the circular protractor, or by the method of chords. 

The Cieculae Peoteactoe. 

146. This instrument consists of a brass circular limb (PL 2, 
Fig. 4), of about six inches in diameter, with a movable index 
AB, having a vernier at one extremity A, and a milled screw 
at the other extremity B, with a concealed cog-wheel that works 
Avith the cogs of the limb, and thus moves the index AB about 
the centre of the protractor. • At the centi'e of the protractor 
is a small circular glass plate, on which two lines are cut; the 
point of their intersection is the exact centre of the instru- 
ment. The limb is generally divided to half-degrees ; the de- 
grees are numbered from to 360. 

At the point, and at the opposite extremities of the 
diameter passing through that point, are small lines on the 
inner edge of the limb ; the two extremities of the diameter, 
perpendicular to this latter, are designated in the same way. 

Two angular pieces of brass, each having a small and 
shai-p steel pin at its extremity, are fastened to the index, and 
revolve freely around the lines ah and cd. The small screws, 
«, J, c, and d, move them in the directions of the lines ab, cd, 
for the purpose of bringing the steel pins exactly into the line 
which passes through the of the index and the centre of 
the protractor. 



182 ELEMENTS OF SUE^TYING. [BOOK II. 

To adjust them to their places, place the centre of the pro- 
tractor oyer a marked point, and the of the index to the 
of the limb. Then mark the place of the index by the pins; 
after which, turn the index 180^, and see if the pins will mark 
the same points as before. If they do, the index is adjusted ; 
if they do not, correct the error with the screws a, h, c, and d. 

To LAY OFP AS" AXGLE WITH THE PeOTKACTOE. 

147. Let its centre be placed over the angular point, and 
the diameter passing through and 180^, on the given line. 
Turn the screw that works the index, until the of the A'ernier 
coincides with the division corresponding to the given angle; 
then let the angular brass pieces be turned down; the points 
dotted by the steel pins will show the direction of the required 
line. 

If this line does not pass through the angular point, the 
pins are out of place, and must be re-adjusted. 

FiEST Method of Plottixg. 

148. Suppose it were required to make the plot of the 
harbor on a scale of 450 yards to an inch. 

Divide the length of the base-line AB, which is equal to 
1140 yards, by 450, and the quotient 2.53 will express the 
length which is to represent the base-line on the paper (Bk. I., 
Art. 39). 

Draw an indefinite line AB, to represent the base; and 
having chosen any point, as A, for the first station, lay off 2.53 
inches to B. The other extremity of the base-line will thus be 
determined. 

Then, place the circular protractor at A, and lay off the 
angle BAU, and then the angle BAG. Xext, place the pro- 
tractor at B, and lay off the angles ABB and BBC. The 



SEC. IV.] CIRCULAR PROTRACTOR. 183 

intersection of the lines AE and BE will determine the station 
E. Let the protractor be then placed at this point, and all 
the angles of station E laid down. 

The point G, w^here EG intersects AG, and the point C, 
where EC intersects BC, will then be found. 

By placing the protractor at C and G, we can determine 
the points D and F, when the place, on the paper, of all the 
stations will be known. 

To unite the work done with the compass, spread the com- 
pass-notes before you, and draw through A a line to represent 
the meridian. The course AE lies to the west of this meridian, 
and makes an angle of 12° with it. 

Then, lay off from the scale the distances Aa, Ab, Aq, Ac, 
Ad, Ae, and at the several points erect perpendiculars to AE. 
Lay off, on these perpendiculars, the lengths of the offsets, 
and the curve traced through the points so determined, will 
be the margin of the lake. 

At E, draw a parallel to the meridian through A, and lay 
down the course Eff, which is easterly, and makes an angle 
of 50° with the meridian. Then, lay down the several distances 
to the offsets, and draw the offsets and lay off their lengths. 
Do the same for the course EI, and all the compass-work will 
be plotted. 

The work done with the plane-table is united to the work 
done with the theodolite, by simply reducing it to the same 
scale, and then placing the line ^iV on the paper of the 
plane-table, upon the line AJS^, drawn on the plot of the 
triangulation. 

Secoin-d Method of Plotti^s-g. 

149. Place the centre of the protractor near the centre of 
the paper, and draw a line through the points and 180°. This 



184 ELEMENTS OF SURVEYING. [BOOK II. 

line will have the same position with the circular protractor 
that the base-line AB had with the limb of the theodolite. 

Then lay off, from the point, an arc equal to the direction 
from A to E, also an arc equal to the direction AG, and 
tlirough the centre point, and the points so determined, draw 
lines. Lay off in succession, in a similar manner, the directions 
taken at all the stations ; and through the centre point, and 
the points so determined, draw lines, and designate each by the 
letters of the direction to which it corresponds. 

Now, since all the lines drawn on the paper have the same 
position with the circular protractor, as the corresponding lines 
on the ground have with the limb of the theodolite, it follows 
that each direction will be parallel to its corresponding line 
upon the ground. 

Hence, any line may be drawn parallel to that passing 
through and 180°, to represent the base-line AB. Having 
drawn such a line, and marked a point for the station A, lay 
off the length of the base, and the extremity will be the 
station B. 

Through A and B, so determined, draw parallels respectively 
to the lines corresponding to the directions AE and BE, and 
the point of intersection will determine station E, Through 
B and E, draw parallels to the lines which correspond to the 
directions BC, CE, and their point of intersection will deter- 
mine station C. Through (7 and E, draw lines parallel to the 
lines corresponding to the directions CE and ED, and the 
point of intersection will determine D. In a similar manner 
we may determine the stations F and G, 

Method op Chords. 

150. The chord of a given arc is equal to the sine of half 
the arc with double the radius. 



SEC. IV.] 



METHOD BY CHORDS. 



185 



For, let DAF be any given angle, 
and AH a line bisectiug it. Let DC 
be the chord of the arc CD, described 
with a given radius, and HF parallel 
to CD, the sine of half the given 
angle, to a radius AF = 2 AC. 

Since AF= 2 AC, we have, from similar triangles, HF-. 
2KC; but DC=2KC, hence HF = CD. 





To LAY OFF AH Als-QLE. 

151. To avoid, as far as possible, the use of fractions, let 
us suppose the radius of the table of natural sines to be 1 ten, 
or 10 inches. 

Take, from a scale, 5 equal parts, 
with which, as a radius, from the 
centre A, describe an arc CD. Take 
from the table the natural sine of 
half the arc, and remove the decimal 

point one place to the right; the result will express the sine 
of half the arc to the radius 10, or the chord of the arc to the 
radius 5. From the same scale, take this sine in the dividers, 
and from C, as a centre, describe an arc cutting CD in D ; 
draw AD, and CAD will be the angle required. 

This is the most accurate of all the methods of laying off 
an angle, and it may also be applied advantageously to the 
second method of plotting, thus: 

Draw a fine straight line, generally in 
the direction of the meridian or of the 
base-line of the survey; and also a line 
perpendicular to it. From the point of 
intersection, as a centre, with a radius 
of 5 equal parts of the scale, describe the 




18 G ELEMENTS OF SUEYEYING. [BOOK II. 

circumference of a circle cutting the straight lines in the points 
marked and 90°. 

To lay off an angle, as, for instance, the angle 14° 29'. 
The half of it is T 14' 30", the natural sine of which is 0.126005, 
or 1.26 to the radius of 10 inches. Set off from to l, as in 
the figure, this distance taken from the scale, and through the 
two points l, h, thus determined, draw a straight line. This 
line should pass through the centre, and will make with the 
line (0, 0) the angle 14° 29' ; and any line on the paper drawn 
parallel to it, will make with the line (0, 0) the same angle. 
The further application is obyious. 

Maeitime Sueveyik"g. 

152. When, in connection with a trigonometrical survey on 
shore, a harbor is to be surveyed, as in the example, for the 
purpose of ascertaining the channels, their depth and w^dth, 
the positions of shoals, and the depth of water thereon, other 
means must be used, and other examinations made, in addition 
to those already described. 

Let buoys be anchored on the principal shoals and along 
the edges of the channel ; and using any one of the lines 
already determined as a base, let the angles subtended by lines 
drawn from its extremities, to the buoys respectively, be meas- 
ured with the theodolite. Then, there will be known, in each 
triangle, the base and angles at the base, from w^hich the dis- 
tances to the buoys are easily found; and hence, their positions 
become known. 

Having made the soundings, and ascertained the exact 
depth of the water at each of the buoys, several points of the 
harbor are established, at which the precise depth of the water 
is known ; and by increasing the number of the buoys, the 
depth of the water can be found at as many points as may 
be deemed necessary. 



SEC. lY.] MARITIME SUEYETING. 187 

153. If a person with a theodolite, or with any other instru- 
ment adapted to the measurement of horizontal angles, be sta- 
tioned at each extremity of the base-line, it will not be neces- 
sary to establish buoys. A boat, provided with an anchor, a 
sounding-line, and a signal-flag, has only to throw the anchor, 
hoist the signal-flag, and make the sounding, while the persons 
at the extremities of the base-line measure the angles. From 
these data, the precise place of the boat can be determined. 

154. There is another method of determining the places at 
which the soundings are made, that admits of great despatch, 
and which, if the obserrations are made with care, affords 
results sufficiently accurate. 

Haying established, trigonometrically, three points which 
can be seen from all parts of the harbor, and having provided 
a sextant, let the sounding be made at any place in the harbor, 
and at the same time the three angles subtended by lines 
drawn to the three fixed points, measured with the sextant. 

The problem, to find, from these data, the place of the boat 
at the time of the sounding, is the same as example 6, p. 93. 

It is only necessary to measure two of the angles, but it is 
safest to measure the third also, as it affords a verification of 
the work. 

The great rapidity with which angles can be measured with 
the sextant, by one skilled in its use, renders this a most expe- 
ditious method of sounding and surveying a harbor. 

The sextant is not described, nor are its uses explained in 
these Elements, because its construction combines many philo- 
sophical principles, with which the Surveyor cannot be sup- 
posed conversant. 

155. There is yet another method of finding the soundings, 
which, although not as accurate as those already explained, 
will, nevertheless, afford results approximating nearly to the 



188 ELEMENTS OF SURVEYING. [BOOK II. 

truth. It is this : — Let a boat be rowed, with uniform speed, 
across the harbor, from one extremity to the other of any of 
the lines determined trigonometrically. Let soundings be made 
continually, and let the precise time of making each be care- 
fully noted. Then, knowing the length of the entire line, 
the time spent in passing over it, as also the time of making 
each of the soundings, we can easily find the points of the 
line at which the several soundings were made ; and hence, 
the depth of water at those points becomes known. 

156. If a person stationed on shore with a theodolite, takes 
the bearing of the boat, at every second or third sounding, de- 
termined by hoisting a flag, it will fix the positions of the sound- 
ings with great accuracy. Soundings may thus be made along 
any number of known lines, and a comparison of the depths 
found, on different lines, at or near their points of intersection, 
will show with what degree of accuracy the work has been done. 

Sounding-lines should be made of strong cord, and divided 
into feet or fathoms, by diff'erent colored rags or other marks. 
The lead is shaped like the frustum of a 
cone, with the base B hollowed out, to hold 
some grease. The land or mud of the bot- 
tom adheres to the grease, and thus shows 
the nature of the bottom, which should be 
entered in the field-book, and laid down 
upon the map. As the cord is liable to 
change its length, it should be compared, 
from time to time, with some standard. 
In tide-waters, the exact time of each sound- 
ing is to be noticed, and an assistant should 
note the height of the tide at regular intervals, upon a tide- 
gauge. The tide-gauge is permanently placed at some con- 
venient point of the harbor, and its point is referred, by 




SEC. IT.] MARITIME SURYEYTNG. 189 

means of a spirit-leyel, to some fixed bench-mark, on a level 
with mean low-water mark, to which all the soundings must 
be reduced. 

157. Haying plotted the work done with the theodolite, as 
also the outline of the harbor traced with the compass, it re- 
mains to delineate the bottom of the harbor; and this is done 
by means of horizontal curves, hereafter explained, (Bk. III., 
Art. 00), w^hich are used to represent broken or undulating 
ground. 

Let the plane of reference be taken through low-water mark, 
or to coincide with the surface of the water, at low tide. The 
accuracy with which the bottom of the harbor is to be delineated, 
will guide us in fixing the distance between the horizontal planes 
of section. 

The first horizontal plane should be passed at a distance 
below the shallowest point that has been sounded, equal to the 
number of feet fixed upon for the distance between the planes 
of section; and the curve, in which it intersects the bottom of 
the harbor, determined as in Book III., Art. 00. And similarly, 
for the other horizontal planes of section. 

Having thus delineated the bottom of the harbor, and noted 
on the map the distance of each intersecting plane below the 
plane of reference, let such lines be drawn as will indicate the 
channels, shoals, sunken rocks, and direction of the current. 

In the example given in Plate 6, soundings have been made 
in three directions, from the sand-bar in the harbor, and also 
from the rocky shore across to the light-house. 



BOOK III. 

LEVELLma AND ITS APPLICATIONS. 



SECTION I. 
OF LEVELLING. 



1. Levellin"G is the art of determining the relative dis- 
tances of points from the centre of the earth. 

2. A line whose points are all equally distant from the 
centre of the earth, is called a line of true level; and a surface, 
all whose points are equally distant from the centre of the 
earth, as the surface of still water, is called a level surface. 

3. One point is said to be above another, when it is farther 
from the centre of the earth; and this difference of distance 
from the centre, is called the difference of level between the 
two points. 

4. A straight line drawn tangent to a line of true level, 
at any point, is a horizontal line, and is called the line of 
apparent level. Thus, (PI. 4, Fig. 1), if C is the centre of the 
earth, and AEFsl line of true level, ABD is the line of apparent 
level. This is the line of level determined by an instrument. 
The difference between the apparent and true of the points 
A and F, is BE, the excess of the secant of the arc AF, over 
the radius. 



f 



SEC. I.] OF LEVELLING. 191 

5. To find a general formula for computing tliis excess, we 
have (Geom., B. IV., Prop. XXX.), 

ZB^ = BE {BE + ^EC) ; 

but, since the arc ^^ is very small in comparison with the 
radius of the earth, the arc AE will not differ sensibly from 
the tangent AB ; the diameter 2^(7 may, for the same reason, 
be taken for the secant {BE + 2EC) : hence, 

~AE' = BEX 2EC, or, dividing by 2EC, 

^^=¥c «• 

If we take the mean diameter of the earth to be 7919 miles, 

AE^ 
formula (1) gives BE = — — - (2), hence, 

Tlie departure of tlie apparent from tlie true level, darting 
from a given point, is equal to the square of the distance to the 
second point, divided iy the diameter of the earth. 

If, in formula (2), we give to AE, in succession, every value 
from 1 chain to any given number of chains (say 100), and 
reduce, at the same time, both terms of the fraction to inches, 
a table may be computed as below. 

Observe, that w^hen the distance AE = 80 chains = 1 mile, 
that BE is = 8.001 inches, or two-thirds of a foot, very nearly ; 
and for any other distance, d, in miles, we have, 

1^ : ^^ :: f of a foot : f^^; 

hence, we have the following easy rule for finding the correc- 
tion of curvature in feet : 

Tlie correction for curvature, in feet, is equal to two-thirds 
of the square of the distaiice in miles. 



192 



ELEMENTS OF SURVEYING. 



[book in. 



Table showing the differences, in inches, between the true and 
apparent level, for distances betw^een 1 and 100 chains. 



Chains. 


Inches. 


Chains. 


Inches. 


Chains. 


Inches. 


Chains. 


Inches. 


1 


.001 


26 


.845 


51 


3.255 


76 


7.221 


2 


.005 


27 


.911 


52 


3.380 


77 


7.412 


o 
o 


.011 


28 


.981 


53 


3.511 


78 


7.605 


4 


.020 


29 


1.051 


54 


3.045 


79 


7.802 


5 


.031 


30 


1.125 


55 


3.781 


80 


8.001 


G 


.045 


31 


1.201 


56 


3.925 


81 


8.202 


7 


.061 


32 


1.280 


57 


4.061 


82 


8.406 


8 


.080 


33 


1.300 


58 


4.205 


83 


8.612 


9 


.101 


34 


1.446 


59 


4.351 


81 


8.832 


10 


.125 


35 


1.531 


60 


4.500 


85 


9.042 


11 


.151 


36 


1.620 


61 


4.654 


86 


9.246 


12 


.180 


37 


l.7il 


62 


4.805 


87 


9.462 


13 


.211 


38 


1.805 


63 


4.968 


88 


9.681 


14 


.245 


39 


1.901 


64 


5.120 


89 


9.902 


15 


.281 


40 


2.003 


65 


5.281 


90 


10.126 


16 


.320 


41 


2.101 


66 


5.443 


91 


10.351 


17 


.361 


42 


2.208 


67 


5.612 


92 


10.587 


18 


.405 


43 


2.311 


68 


5.787 


93 


10.812 


19 


.451 


44 


2.240 


69 


5.955 


94 


11.046 


20 


.500 


45 


2.531 


70 


6.125 


95 


11.233 


21 


.552 


46 


2.646 


71 


6.302 


96 


11.521 


22 


.605 


47 


2.761 


72 


6.480 


97 


11.763 


23 


.661 


48 


2.880 


73 


6.662 


98 


12.017 


24 


.720 


49 


3.004 


74 


6.846 


99 


12.246 


25 


.781 


50 


3.125 


75 


7.032 


100 


12.502 



Iksteuments. 

6. Before proceeding further in the discussion of the prin- 
ciples of leyelling, we will describe some of the instruments 
used, and first, 

The Y Level. 

7. A Level is an instrument used to indicate a horizontal 
line, and also, to determine the difference of level of any two 
points on the surface of the earth. 



SEC. I.] THE Y LEYEIi. 193 

The part of the instrument shown in (PL 4, Fig. 2), rests 
on a tripod, to which it is permanently attached at Z. HE 
is a horizontal brass plate, through which four levelling-screws 
with milled heads are passed, and worked against a second 
horizontal plate, GG. Two of these screAvs, K and /, are seen 
in the figure. iS' is a clamp-screw, which, being loosened, allows 
the upper part of the instrument to turn freely around its 
axis. Q is a tangent-screw, by means of which the upper part 
of the instrument is moved gently, after the clamp-screw S has 
been made fast. EE is a horizontal bar, perpendicular to which 
are the wyes, designated Y's, that support the telescope LB. 
This telescope is confined in the Y's by the loops r, r, which, 
are fastened by the pins p and p. The object-glass B, is adjusted 
to its focus by the screw X, the eye-glass L slides out and 
in, freely. The screws /, /, work the slide which carries the 
horizontal hair; and two horizontal screws, only one of which, 
a, is seen, work the slide that carries the yertical hair. CD is 
an attached spirit-leyel. The screw N elevates and depresses 
the Y nearest the eye-glass. In some instruments this Y is 
elevated and depressed, by means of two screws at M and M, 

Before using this level, it must be adjusted. The adjust- 
ment consists in bringing the different parts to their proper 
places. 

The line of CGlUmation is the axis of the telescope. With 
this axis, the line drawn through the centre of the eye-glass 
and the intersection of the spider's lines, within the barrel of 
the telescope, ought to coincide. 

First ADJusT:^iEis-T. 

To fix the intersection of the spider's lines in the axis of the 

telescope. 

8. Having screwed the tripod to the instrument, extend the 

legs, and place them firmly. Then loosen the clamp-screw S, 

13 



194 ELEMENTS OF SURVEYDTG. [BOOK III. 

and direct the telescope to a small, well-defined, and distant 
object. Then slide the eye-glass till the spider's lines are seen 
distinctly; after which, with the screw X, adjust the object-glass 
to its proper focus, when the object and the spider's lines will 
be distinctly seen. Note now the precise point covered by the 
intersection of the spider's lines. 

Having done this, revolve the telescope in the Y's, half 
round, when the attached level CD will come to the upper side. 
See if, in this position, the horizontal hair appears above or 
below the point, and in either case, loosen the one, and tighten 
the other, of the two screws which work the horizontal hair, 
until it has been carried over half the space between its last 
position and the observed point. Carry the telescope back to 
its place; direct again, by the screws at 3f and R, the inter- 
section of the spider's lines to the point, and repeat the opera- 
tion, till the horizontal hair neither ascends nor descends while 
the telescope is revolved. A similar process will arrange the 
-vertical hair, and the line of collimation is then adjusted. 

SECOiy'D Adjustment. 

To make the axis of the attached level CD parallel to the line of 

collimation. 

Turn the levelling-screws M and R, until the bubble of the 
level DC stands at the middle of the tube. Then open the 
loops, and reverse the telescope. If the bubble still stands at 
the middle of the tube, the axis of the level is horizontal; but 
if not, it is inclined, the bubble being at the elevated end. In 
such case, raise the depressed, or depress the elevated end, by 
means of the small screw h, half the inclination ; and then with 
the screws, at M and R, bring the level to a horizontal position. 
Reverse the telescope in the Y's, and make similar corrections 
again ; and proceed thus, until the bubble stands in the middle 



SEC. I.] THE Y LEVEL. 195 

of the tube, in both positions of the telescope ; the axis of the 
leyel is then horizontal. 

Let the telescope be now reyolved in the Y's. If the bubble 
continues in the middle of the tube, the axis of the level is not 
only horizontal, but also parallel to the line of collimation. If, 
however, the bubble recedes from the centre, the axis of the 
level is inclined to the line of collimation, and must be made 
parallel to it, by means of two small screws, which work hori- 
zontally; one of these screws is seen at q. By loosening one 
of them, and tightening the other, the level is soon brought 
parallel to the line of collimation ; and then, if the telescope be 
revolved in the Y's, the bubble will continue at the middle of 
the point of the tube. It is, however, difficult to make the 
first part of this adjustment, while the axis of the level is con- 
siderably inclined to the line of collimation; for, even if the 
level be truly horizontal in one position of the telescope, after 
it is reversed, there will be but one corresponding position in 
which the bubble will stand at the middle of the tube. This 
suggests the necessity of making the first part of the adjust- 
ment with tolerable accuracy; then, having made the second 
with care, re-examine the first, and proceed thus till the adjust- 
ment is completed. 

Third Adjustmeio'. 

To make the level CD and the line of collimation perpendicular to 
the axis of the instrument, or parallel to the horizontal bar EE. 

Loosen the clamp-screw 8, and turn the bar EE, until the 
level DO comes directly over two of the levelling screws. By 
means of these screws, make the level CD truly horizontal. 
Then, turn the level quite round; if, during the revolution, it 
continue horizontal, it must be at right angles to the axis of 
the instrument about which it has been revolved. But if, after 



196 ELEMENTS OF SUKYEYDsG. [BOOK m. 

the revolution, the level CD be not horizontal, rectify half the 
error witli the screws at J/ and B, and half with the levelling 
screws. Then place the bar EE over the other two levelling 
screws, and make the same examinations and corrections as 
before ; and proceed thus, until the level can be turned entirely 
around without displacing the bubble at the centre. When this 
can be done, it is obvious that the level DC and the line of 
collimation, are at right angles to the axis of the instrument, 
about which they revolve; and since the axis is carefully ad- 
justed by the maker, at right angles to the bai* EE, it follows, 
that the line of collimation, the level DC, and the bar EE, are 
parallel to each other. 

The level is now adjusted. TThen used, however, it is best 
to re-examine it every day or two, as the work will be erroneous 
unless the instrument is accurately adjusted. 

LeyellixCt Eods. 

9. The levelling rods are used to determine the points at 
which a given horizontal line intersects lines that are perpen- 
dicular to the surface of the earth, and to show the distances 
of such points of intersection from the ground. 

There are two kinds of rods used by engineei*s, known as 
the Boston and Xew York rods. 

They are both sliding rods, divided into feet, tenths, and 
hundredths of feet ; and the readings, by means of a vernier, are 
made to thousandths of a foot. 

10. The Boston Eod is fonned by two pieces of hard wood, 
about six feet and a half in length, the one sliding through 
grooves, along the other, in both directions. 

A vane or target, six-tenths of a foot in width, divided into 
four equal rectangles by a horizontal and vertical line, passing 



SEC. I.] 



NEW YOEK ROD. 



197 



through the centre, is permanently connected with one ex- 
tremity of the sliding piece. The two diagonal rectangles of 
the target, are usually painted black or red, and 
the other two white, so that the centre and the 
horizontal dividing line, may be distinctly seen. 

There are two yerniers, one at either end of 
the second piece, by means of which the read- 
ings, indicating the height of the target, are read. 

When the height is less than six feet, the 
reading is made by the yernier at the top of the 
rod; and when it is greater than six feet, the 
rod is reversed, which brings the other vernier 
to the top ; the target is then run up to the re- 
quired height, and the reading made as before. 



New York Rod. 



^ 



11. This rod, which is shown in the en- 
graving, is cut in two parts, so that, both ends 
may be exhibited. It is made of satin-wood, 
in two pieces, like the former, but sliding one 
from the other, always in the same direction, 
so that the same end is always held on the 
ground, and the graduations start from that M 
point. In this rod, as in the other, a target ' 
is used to indicate where the horizontal line 
cuts the rod. 

The face of the target is divided into quad- 
rants, by a horizontal and a vertical diameter; 
and these diameters are the boundaries of the 
alternate colors with which the diagonal quad- 
rants are painted. 

The opening, in the face of the target, is a little more 
than the tenth of a foot. The right edge of the opening is 



J-^^ ELEMENTS OF SURVEYING. [BOOK in. 

chamfered, and divided into ten equal spaces, corresponding to 
nine hundredths on the rod: hence, the vernier reads to thou- 
sandths of a foot. For heights less than six feet, the target is 
moved along the sliding part, to Avhich it is slightly attached 
by springs, and to which it may be permanently attached by 
a clamp-screw, and the reading is made by the vernier on the 
target. "When the height exceeds six feet, the slide and target 
are run np to the requisite height, and the reading is made 
by the vernier at the top of the staff. 

Tests of Adjustment. 

12. There is a method of testing the adjustments of the 
Y level, which ought not to be neglected, since all the results 
depend on the accuracy of the instrument. The method is 
this: 

The level being adjusted, place it at any convenient point, 
as G (PI. 4, Fig. 4). At eqnal distances of about 100 yards, on 
either side, and in the same line with the level, place the 
levelling rods, Cb, BF. Make the level horizontal with the 
levelling screws. Then, turn it toward either rod, as BF, and 
run the vane np or down, as required, until the intersection 
of the hairs strikes the centre : then make the slide fast, and 
note carefully the height of the vane. Turn the level half 
round, and do the same in respect of the staff CI. 

Let the telescope be now reversed in the Y's. Sight again 
to the rod BF, and note the exact height of the vane. Let 
the telescope be now turned half round, and the same be done 
for the rod Ch. \i the two heights last observed are equal 
to those first noted, each to each, the line of collimation is 
perpendicular to the axis of the instrument; and if the bubble 
has, at the same time, preserved its place at the middle point 
of the tube, the instrument is truly adjusted. 



SEC. I.] LEVELLING. 199 

For, had the line of collimation been inclined to the axis 
of the level, it would, in the first instance, have taken the 
direction AF or Ad; and when turned half round, it would 
have taken the direction AE or Ad. The telescope being re- 
versed in the Y's, and again directed to the staff BF, the line 
of collimation would take the direction Ad or AF, and when 
turned to the staff Ch, it would take the direction Ah oy AF: 
and the two distances BF, Bd, or Cb, CE, can only be equal 
to each other when the line of collimation falls on the hori- 
zontal line gf, 

LeVELLIKG IK THE FlELD. 

13. The operations of levelling may be undertaken : 

1st. For the purpose of determining the difference of level 
between two given points: 

2d. For the purpose of obtaining a section or profile along 
a given line, as in the preliminary surveys for railroads and 
canals : 

3d. For the purpose of determining the contour lines in a 
topographical survey, as described in Section II.; and, 

stilly. For the purpose of determining the volume of any 
given mass of earthwork or masonry; as the measurement of 
excavations and embankments for canals and railroads: and, 

5thly. For the purpose of determining and indicating bound- 
aries for filling and excavation; such as setting stope stakes, 
&c. 

DlEFEEEKCE OF LeVEL BETWEEN" TWO PoiNTS. 

14. When it is proposed to find the difference of level of any 
two objects, or stations, all levels made in the direction of -the 
station at which the work is begun, are called, for the sake of 



200 



ELEMENTS OF SURVEYING. 



[book m. 



distinction merely, lach-sigUts ; and levels taken in the direc- 
tion of the other station, fore-sights. 

Before going on the field with the level, rule three columns, 
as below, and head them, stations, back-sights, fore-sights. 

Field Notes. 



stations. 


+ Back-sights. 


— Fore-Sights. 


1 

2 
3 


10 
11.6 

6.8 
3.9 


3 



4.9 

8.3 


Sums -32.3 

16.2 
Dif. of level . . 16.1 


16.2 



EXAMPLES. 

Find the difference of level between any two points, 
as A and G (PL 4, Fig. 5). 

The level being adjusted, place it at any point, as B, as 
nearly in the line joining A and G, as may be convenient. 
Place a levelling rod at A. Make the level horizontal by means 
of the levelling screws ; turn the telescope to the rod at A, and 
direct the rodman to raise the target until the horizontal line 
ab pierces its centre; then note the distance Ab (equal to 10 
feet in the present example) and enter it in the column of 
back-sights opposite station 1. 

Send the rodman forward to some point, as iV", in the pro- 
posed direction, and sight to the rod as before; enter the dis- 
tance iV«, equal to 3 feet, in the column of fore-sights opposite 
station 1, (B). Then remove the level to a convenient point, 
as C, (2). Direct the rodman to run up the vane to the proper 
height ; then make the back-sight, and enter it, JS^d = 11.6 feet, 



SEC. I.] LEYELLIXG. 201 

in the column of back-sights, opposite station 2. Let the rod- 
man then be sent forward to a convenient point, as J/, and 
make the fore-sight to /; and enter Mf = 0, in the column of 
fore-sights, opposite station 2, (C). Eemoye the level, in succes- 
sion, to D and B, and make similar levels at those points, and 
enter the results in the columns of back-sights and fore-sights, 
opposite stations 3, (D), and 4, (E). 

It is evident from the figure, that the difference of level ^F, 
between A and X, is equal to the back-sight dA, diminished by 
the fore-sight aXj also that the difference of level between 
Ji and J/, is equal to the back-sight ciy, diminished by the 
foresight 0, and since each set of observations is entirely inde- 
pendent of every other set. we may infer that the difference of 
level leticeen two consecutive points, as determined l)y tlie same 
position of the level, is equal to tlie lacTc- sight, diminished lij tTie 
fore-sight. If the fore-sight be greater than the back-sight, the 
difference will be affected with a minus sign, a restilt which 
shows that the second point is lower than the first : and. 

Generally, the difference of level letv;een any two points, deter- 
mined as above, is equal to tlie sum of the ladc-sights diminished 
hj the sum of the fore-sights. If the result is plus, the second 
point is higher than the first ; if negative, it is lower. 

In the example given, the difference of level between A and 
G^, is 16 feet and 1 tenth. 

15. In the above example, we did not regard the difference 
between the true and apparent level. If it be necessary to 
ascertain the result with extreme acctiracy, this difference must 
be considered: and then, the horizontal distances between the 
level, at each of its positions, and the rods, must be measured, 
and the apparent levels diminished by the differences of level; 
which differences can be found from the table. 



202 



ELEMENTS OF SUKVEYING. 



[book m. 



EXAMPLE. 



Stat. 

1 
2 

3 

4 
5 


Back-sts. 


Distances. 


Fore-st. 


Distances. 


Cor. back-sts. 


Cor.for-sts. 


9.8 

8.7 

5.2 

10.3 

11.0 


20 ch. 

25 ch. 
18 ch. 
29 ch. 
45 ch. 


1.6 
2.4 
3.1 
1.9 
2.5 


32 ch. 
28 ch. 
16 ch. 
87 ch. 
72 ch. 


9.7583 

8.6349 

5.1663 

10.2124 

10.7891 


1.4933 
2.3183 
3.0734 
0.1115 
1.9600 




44.5610 


8.9565 



In this example, the first column shows the stations; the 
second, the back-sights; the third, the distances from the level 
in each of its positions to the back rod; the fourth, the fore- 
sights; the fifth, the distances from the leyel to the forward rod; 
the sixth and seventh, are the columns of back and fore sights, 
corrected by the difference of leyel. The corrections are thus 
made: The difference of level in the table corresponding to 20 
chains, is 5 tenths of an inch, or .0417 of a foot nearly; which 
being subtracted from 9.8 feet, leaves 9.7583 feet for the corrected 
back-sights; this is entered, opposite station 1 in the sixth 
column. The difference of level corresponding to 32 chains, is 
1.280 inches, or .1067 feet, nearly; which being subtracted from 
the apparent level, 1 foot 6 tenths, leaves 1.4933 feet, for th6' true 
fore-sight from station 1. The other corrections are made in 
the same manner. 

The sum of the back-sights being 44.5610 feet, and the 
sum of the fore-sights 8.9565 feet, it follows, that the difference, 
35.6045 feet, is the true difference of level. 



16. In finding the true from the apparent level, we have 
not regarded the effect caused by refraction on the apparent 
elevation of objects, as well because the refraction is different 



SEC. I.] LEVELLING. 203 

in different states of the atmosphere, as because tlie correc- 
tions are inconsiderable in themselves. 

17. The small errors that would arise in regarding the 
apparent as the true level, may be avoided dy i^lacing tlie level- 
ling rods at equal distances from the level. In such case, it is 
plain, 1st, that equal corrections must be made in the fore 
and back-sights ; and, 2dly, that when the fore and back- 
sights are diminished equally, the result, which is always the 
difference of their sums, will not be affected. 

This method should always be followed, if practicable, as 
it avoids the trouble of making corrections for the difference 
of true and apparent level. 

The differences between the true and apparent level, being 
very inconsiderable for short distances, if only ordinary accuracy 
be required, it will be unnecessary to make measurements at 
all. Care, however, ought to be taken, in placing the levelling 
rods, to have them as nearly equidistant from tlie level as can 
be determined by the eye; and if the distances are unequal, 
let the next distances also be made unequal ; that is, if the 
back-sight is the longer in the first case, let it be made pro- 
portionably shorter in the second, and the reverse. 

LEYELLIis-G FOK SeCTIO:S". 

18. Having decided upon the line along which a section is 
to be taken, let a permanent mark be made at the beginning 
of the line : this is called, a hench-mark. A bench-mark is made 
by drilling a hole in a rock, or by painting upon a rock or 
fence, or sometimes by driving a stake in the ground, with its 
upper end marked by a nail-head. Bench-marks should be 
made from time to time along the line, to serve as checks, in 
case a re-survey should become necessary. 



20-1 



ELEMENTS OF SURVEYING. 



[book in. 



The operations in the field are similar to those in the last 
example, and the field-notes are kept in the same manner, 
except that a new column is added for bearings, when it is 
necessary to make a plot of the line of survey. The total 
distance of each point, above or below the starting-point, may 
be computed, and written in a separate column, paying par- 
ticular attention to the signs. We annex an example, in which 
the heights are estimated in feet, and decimals of a foot. 

EXAMPLE. 



sta- 
tion. 


Distances 
in feet. 


B. Sight. 


F. Sight. 


Dif. between 
B. S. and F. S. 


Total Dif. of 
Level. 


Kemakks. 


1 


650 


2.35 


14.55 


- 12.20 


- 12.20 


Commenced at hench-mark A. 


2 


700 


3.56 


9.58 


- 6.02 


- 18.22 




3 


750 


10.34 


6.21 


+ 4.13 


- 14.09 




4 


650 


14.55 


0.25 


+ 14.30 


+ 0.21 




5 


600 


9.98 


1.67 


+ 8.31 


+ 8.52 




6 


650 


3.62 


14.54 


- 10.92 


- 2.40 






B.M. 


1.23 


13.45 


- 12.22 


- 14.62 


Bench-mark on rock. 


7 


500 


2.23 


- 12.05 


- 9.82 


- 24.44 


Terminating at B. HT. on oak- 


8 


750 


6.20 


19.55 


- 13.35 


- 37.79 


tree. 



The fifth column shows the diflTerence of level between any 
two consecutive positions of the levelling rod, and is found by 
subtracting the fore-sight from the corresponding back-sight, 
and giving to the remainder the proper sign. The sixth column 
shows the distance of each point, above or below the bench- 
mark A, and is obtained by continual additions of the numbers 
in column 5. Thus, 



(-12.20) + (-6.02) 
and so on. 



- 18.22; (- 18.22) + 4.13 = - 14.09; 



It will be seen that the point of termination is 37.79 feet 
"below the starting-point. 



SEC. I.] 



LEVELLING. 



205 



Profile of Sectioi^. 

19. The vertical distances being generally very small as 
compared with the horizontal distances, two different scales be- 
come necessary in plotting a profile. In order that the vertical 
distances may be fully exhibited in the plan, the scale used for 
them is much larger than is used for the horizontal lines. 
This becomes absolutely necessary where long lines of profile, 
with a gentle slope, are to be plotted, as is always the case 
in the trial section of a railroad suryey. We shall illustrate 
the manner of plotting a profile section, by drawing the section 
determined by the field-notes just given. 

20. Draw a horizontal line AK, called a datum line, and 
assume some point as A, to represent the point of beginning: 
lay ofi", on the datum line, distances equal to the measured 



650 



^ ^/'''^^m 



■B__ Y00_ _C _750 D 650 _^^ioO J.^e^^y G 500 H___7_5q__K 




distances 650, 700, 750, &c., feet to K, using in this case a scale 
of 1500 feet to 1 inch. At the points B, C, D, E, &c., thus 
determined, erect perpendiculars, making them equal, on a scale 
of 25 feet to the inch, to the corresponding difi'erences of level 
taken from the field-book ; through the points thus found, draw 
the irregular line APLM, and it will represent the surface of 
the ground along the line of level. 



206 ELEMENTS OF SURVEYING. [BOOK m. 

The bench-mark, between stiitions 6 and 7, is not plotted, 
as it is supposed to be out of the line of the section, and no 
distances are measured to it. 



SECTION n. 

TOPOGRAPHICAL SURVEYING. 



21. Besides the surveys that are made to determine the 
area of land and the relative positions of objects, it is frequently 
necessary to make minute and careful examinations for the 
purpose of ascertaining the form and accidents of the ground, 
and to make such a plan as will distinguish the swelling hill 
from the sunken valley, and the course of the rivulet from 
the unbroken plain. 

This branch of surveying is called Topography. In surveys 
made with a view to the location of extensive works, the de- 
termination of the slopes and irregularities of the ground is 
of the first importance : indeed, the examinations w.ould other- 
wise be useless. 

22. The manner of ascertaining these irregularities is, to 
suppose the surface of the ground to be intersected by a 
system of horizontal planes at equal distances from each other; 
the curves determined by these secant planes, being lines of 
the surface, will indicate its form, at the places of section, 
and, as the planes are nearer or more distant from each other, 
the form of the surface will be, more or less, accurately ascer- 
tained. 

If such a system of curves be determined, and then pro- 
jected or let fall on a horizontal plane, it is obvious that the 
curves on such plane w^ill be nearer together or farther apart, 
as the ascent of the hill is steep, or gentle. 



SEQ. n.] TOPOGRAPHICAL SUEYEYING. 207 

If, therefore, such intersections be made, and the curves so 
determined be accurately delineated on paper, the map will 
give such a representation of the ground as will show its form, 
its inequalities, and its striking characteristics. 

23. The subject divides itself, naturally, into two parts: 

1st. To make the necessaiy examinations and measurements 
on the field; and, 

2d. To make the plot, or the delineations on paper. 

For the former of these objects, the theodolite is the best 
instrument; the common level, however, will answer all the 
purposes, though it is less convenient. 

24. Before going on the field, it is necessary to provide a 
number of wooden stakes, about two feet in length, with heads. 
These stakes are used to designate particular points, and are 
to be driven to the surface of the ground. A nail should then 
be driven into the head of each of them, to mark its centre. 

We shall, perhaps, be best understood, by giving an example 
or two, and then adding such general remarks as will extend 
the particular cases to all others that can occur. 

ExAiTPLE First. 

25. Let A, (PL 4, Fig. 6), be the summit of a hill, the contour 
of which it is required to determine and represent. At A, let a 
stake be driven, and let the axis of the theodolite, or level, be 
placed directly over the nail which marks its centre. From Ay 
measure any line down the hill, as AB, using the telescope of 
the theodolite, or level, to arrange all its points in the same 
vertical plane. Great care must be taken to keep the measuring 
chain horizontal, for it is the horizontal distances that are re- 
quired. At different points of this line, as «, d, c, d, &c., let 



208 



ELEMENTS OF SUKYEYING. 



[book m. 



stakes be driven, and let the horizontal distances A a, ab, he, 
and cdy be carefully measured. In placing the stakes, reference 
must be had to the abruptness of the declivity, and the accuracy 
with which the surface is to be delineated: their differences of 
level ought not to exceed once and a half, or twice, the distance 
between the horizontal planes of section. 

Having placed stakes, and measured all the distances along 
the line AB^ run another line down the hill, as AC, placing 
stakes at the points e, f, g and li, and measuring the horizontal 
distances Ae, ef, fg, and gli. Eun also the line AD, placing 
stakes at i, I, m, and n, and measuring the horizontal distances 
Ai, il, Im, and mn. 

Each line, AB, AC, AD, running down the hill, from A, 
may be regarded as the intersection of the hill, by a vertical 
plane; and these secant planes are to be continued over all the 
ground which is to be surveyed. If the work is done with a 
theodolite, or with a level having a compass, the angles DAB 
and BAC, contained by the vertical secant planes, can be 
measured; if it is done with a level, having no needle, let any 
of the distances ae, hf, ai, hi, &c., be measured with the chain, 
and there will then be known the three sides of the triangles 
Aae, Ahf, Aai, Ahl, &c. 

Let, now, the difference of level of all the points marked in 
each of the lines AB, AD, AC, be determined. 

In the present example the results of the measurements and 



levelling, are — 








Line 


AB. 


Distances. 




Difference of Level. 


Aa = 40 feet 




A above a 12 feet 


ad =50 " 




a above ^ 8 " 


he =30 " 




h above c 9 " 


cd =46 « 




c above d 11 " 



SEC. n.] TOPOGRAPHICAL SrEYEYINQ. 209 

Line AC. 
Distances. Difference of Leyel. 



Ae = 28 feet 
ef =45 - 
fg =o5 " 
gJi =49 " 



A above e, 11 feet 

e above /, 9 " 

/ above g, 12 " 

g above 7i, 14 ^^ 



Line ^Z). 
Distances. Difference of Level. 



Ai =25 feet 
il =55 " 
Im = 38 *•' 
W7i=48 " 



A above /, • 9 feet 

I above /, 13 " 

I above ??2, 7 " 

7n above n, 14 " 



Angle CAB = 25^ Angle DAB = 30°. 

These data are sufficient, not only to find the intersections 
of horizontal planes with the surface of the hill, but also for 
delineating such curves of section on paper. 

Plot op Woek. 

Having drawn, on the paper, the line AB, lay off the angle 
BAC = 25°, and the angle BAD = 30°. Then, from a conven- 
ient scale of equal parts, lay off the distances Aa, ai, ic, cd, 
Ae, ef, fg, gli, Ai, il, hn, and mii. 

Let the horizontal planes be passed at a distance of eight 
feet from each other. Since A is the highest point of the hill, 
and the difference of level of the points A and a, is 12 feet, the 
first plane, reckoning downwards, will intersect the line traced 
on the ground from A to B, between A and a. Regarding the 
descent as uniform, which we may do for small distances, without 
sensible error, we have this proportion : as the difference of level 
of the points A and a, is to the horizontal distance Aa, so is 8 
feet, to the horizontal distance from A to where the first hori- 
zontal plane will cut the line from A to B, This distance being 
thus found, and laid off from A to o, gives o, a point of the 



;210 ELEMENTS OF SURVEYING. [BOOK HI. 

curve in wliicli the first plane intersects the ground. The 
points at which it cuts the line from A to C, and the line from 
A to D, are determined similarly, and three points in the first 
curve are thus found. 

The graphic operations are greatly facilitated by the aid of 
the sector. Let it be borne in mind, that the descent from 
A to a, is 12 feet, and that it is required, upon the supposition 
of the descent being uniform, to find that part of the distance 
corresponding to a descent of 8 feet. Take the distance from 
A to a, in the dividers, and open the arms of the sector until 
the dividers will reach from 12 on the line of equal parts, on one 
side, to 12 on the line of equal parts, on the other. Then, 
without changing the angle, extend the dividers from 8 on one 
side, to 8 on the other ; this will give the proportional distance 
to be laid off from A to o. Or, if the dividers be extended 
from 4 to 4, the proportional distance may be laid ofiT from a to o. 

If the distances to be taken from the sector fall too near the 
joint, let multiples of them be used; as for instance, on the 
French sectors, let the arms be extended until the dividers 
reach from 120 on the one, to 120 on the other, then 80 or 40 
"will be the proportional numbers. Other multiples may be used, 
though it is generally more convenient to multiply by 10. 

20. The second plane is to pass 8 feet below the first, 
■that is, 16 feet below A, or 4 feet below a, a being 12 feet 
'below A. Take the distance ab, in the dividers, and extend 
'the sector, so that the dividers will reach from 8 to (the 
'descent from a to i being 8 feet) 8, or from 80 to 80; then, 
the distance from 4 to 4, or from 40 to 40, being laid off 
■from a to p, gives p, a point of the second curve. 

The difference of level between a and 5, being 8 feet, and 
the difference of level between a and j9, being 4 feet, the dif- 
ference of level between p and d, must also be 4 feet; hence, 



SEC. n.] 



TOPOGRAPHICAL SURVEYING. 



211 



the third plane will pass 4 feet below I, and q^ determined 
as above, is a point of the third curve, and so on. After 
having determined the points in which each contour line cuts 
the lines diverging from A, let the contour lines be drawn 
through them, so as to indicate the surface of the hill. The 
numbers (8), (16), &c., show the vertical distances of the re- 
spective planes below the point A, 

27. Having drawn the horizontal curves, the next thing to 
be done is so to shade the drawing that it may represent accu- 
rately the surface of the ground. This is done by drawing 
a system of small broken lines, as in the figure, perpendicular 
in direction to the horizontal curves already described. In all 
topographical representations of undulating ground, the lines 
of shading are drawn perpendicular to the horizontal curves. 

A profile along either of the diverging lines may be plotted 
by the rules already given (Art. 20). The diagram shows the 
profile along the line AB. 




Bd 



Example Secokd. 

28. The following example will illustrate the methods em- 
ployed in making a topographical survey, where great accuracy 
is required. 

By means of a theodolite or level, range a line of stakes 
A, B, C, D, E, &c., along one side, or through the middle of the 
ground to be surveyed, at equal and convenient distances from 
each other, say 50 feet apart. Mark, with a piece of red chalk, 
on each stake in this row, one of the letters of the alphabet, 



212 



ELEMENTS OF SUEVEYING. 



[book m. 



A, B, C, D, Ef &c., in their order. At A, range a line of stakes, 
perpendicular to AE, planting the stakes at intervals of 50 
feet ; and mark them with the letters ^> ^> ^> &c., which are 

1, 2, 3, ' 

read A first, A second, A third, &c. ^ 



J5 



D 



A 

1 


i 


A 
3 


i i 


B 

1 


3 
Z 


B 
3 

h 


J} B 

4, i 


c 

1 


C 

2 


C 
3 


c c 

4 £ 


2 
El 


J) 
Z 

m 


D 

3 

a 

.E3 


D J) 
4 S 

14 Hj 



At i?, range a line of stakes also perpendicnlar to AE, and 
at distances of 50 feet from each other, and designate them 

■?' ■?' ?' ^^' -^^ ^^® ^^^® ^^ ^' -^f ^' ^^'f ^^^^^ ^^^ *^^^ stakes 
are placed, dividing the area, to he surveyed, into squares of 50 
feet on a side. The letters and figures should be plainly marked 
on a smooth face of each stake, for facility of reference. If this 
system of notation be followed, the stakes may be recorded 
without danger of confusion. 

The next operation is to determine the difference of level 
between each stake, and some fixed horizontal plane, which is 
called 2b plane of reference. If the sea is near, the plane of mean 
low water, may be taken as the plane of reference. If not, 
assume the horizontal plane, passing through the lowest point 



SEC. n.] 



TOPOGRAPHICAL SURVEYING. 



213 



of the ground to be surveyed, and make a permanent bench- 
mark at the point of beginning. If the lowest point cannot 
be easily determined, assume such a plane of reference as shall 
pass quite below the lowest point of the ground. 

The following is the form of a field-book, used in topo- 
graphical levelling. 

Field Is'otes. 



Back-sights. 


Fore-sights. 


Difference. 


Total dif. of level 
above E 3 


Bexabks. 


Olqect. 


Beading. 


Object. 


Reading. 




Object 
E3 


Beading. 
0.000 




E3 


11.432 


D3 


1.211 


+ 10.221 


D3 


10.221 








04 


0.S97 


-1- 0.314 


C4 


10.535 


Check 10.535 


C4 


11.112 


E2 


5.281 


+ 5.831 


E2 


16.366 








E4 


6.154 


- 0.873 


E4 


15.493 








D4 


&.001 


+ 0.153 


D4 


15.646 








D2 


1.1S2 


+ 4.819 


D2 


20.465 








C3 


2.917 


- 1.735 


C3 


18.730 








B5 


6.080 


— 3.163 


B5 


15.567 








C5 


0.921 


-f 5.159 


C5 


20.726 




B4 


11.8S2 


B4 
El 


0.113 
8.019 


+ 0.S08 
+ 3.863 


B4 
El 


21.5a4 
25.397 


Check 10.999 
21.534 






B3 


3.990 


+ 4.029 


B3 


29.426 








Dl 


4.118 


- 0.128 


Dl 


29.298 








02 


1.8S0 


+ 2.238 


02 


31.536 








A4 


5.000 


- 3.120 


A4 


28.416 








A5 


9.928 


— 4.928 


A5 


23.488 








D5 


1.675 


+ 8.253 


D5 


31.741 






' 


E5 


1.111 


+ 0.564 


E5 


32.305 








A3 


0.108 


+ 1.003 


A3 


a3.308 








CI 


0.004 


+ 0.104 


01 


33.412 


Check 11.878 


01 


11.149 


B2 


4.181 


+ 6.968 


B2 


40.380 


33.412 






Bl 


2.008 


+ 2.173 


Bl 


42.553 








A2 


0.817 


-f- 1.191 


A2 


43.744 


Check 10.a32 
43.744 


A2 


10.102 


Al 


4.332 


-t- 5.570 


Al 


49.514 


Check 5.770 
49.514 



214: ELEMENTS OF SURVEYING. [BOOK III. 

In the example, which we have taken for ilhistration, the 
stake ^y is the lowest point, and let us assume the plane of 
reference to pass through that point. 

Set up the level at some convenient point, as a, take the 
reading of a leyelling rod, set up at ^> (11.432), and enter this 
reading as a back-sight. Then take the readings of the rod, 
placed at as many stakes as can be reached from the position 
a of the level, entering them as fore-sights, and endeavor to 
make the last reading as small as possible. At this last stake, 
Y> drive a small peg for a bench-mark, or check. 

If we subtract the fore-sight, (^)> (1.211), from the back- 
sight (^)j (11.432), the difference, (10.221), is entered in the 
column headed difference. But this is not only the difference 
of level between (^) and (^)> but is also the height of 
\P), (10.221), above the plane of reference through (^) : hence, 
we enter this difference, under the column, headed total diff. 
of level, as well as in the column of differences for any two 
consecutive stations. If, now, we subtract the fore-sight (^)j 
(0.897), from the fore-sight {D), (1.211), the difference, (0.314), 
is evidently the height of (^) above (^) ; and if we now add 
this difference to the previous total, (10.221), we shall have 
the height of (^ above (f )^ (10.535). 

Move the level to a second point h, and take a back-sight 
to the bench-mark, (C4), and fore-sights, to as many stakes as 
possible. 

Subtracting the fore-sight (^)> (5.281), from the back- 
sight (^)? (11.112), we get the difference of level between 
{^) and (^)> (5.831) ; this being added to the previous 
total, gives the height of \^) above the plane of reference, 
through (^)? — namely, 16.366 feet. In subtracting the 
fore-sight (f )^ (6.154), from the fore-sight (■^)> (5.281), 
we find a negative result, (— 0.873 ), which shows that 



SEC. II.] TOPOGRAPHICAL SURYEYING. 215 

(^) is below i-^j- "We then enter this difference, with its 

4 2 

negative sign, in the colnmn of differences : and to get the 
total, ice add it, luith its algebraic sign, to the preyious total, 
giving (15.493), and so on, for the remaining parts of the 
examjDle. 

As a check on the accuracy of our computation, subtract 
the fore-sight (C'4) from the back-sight (^3), and the differ- 
ence will give the height of (C4), (10.535), above the plane 
of reference. 

Again, subtract the fore-sight (^4) from the back-sight 
(C4), and add the remainder to the height of (C4), and we 
shall find the height of (^4), (21.534), which should agree 
with the height found under the heading, total diff. of level; 
and so on for each time the level is moved. Each back-sight 
indicates a new position of the level. 

Plotting the TToek. 

29. Draw, on a piece of paper, a straight line AE. From 
a scale of equal parts, set off distances AB, BC, &c., each 
to represent 50 feet. Erect perpendiculars to AE, at each of 
the points A, B, C, &c., and then set off the distances fi*om 
A to 2, from 2 to 3, &c., each to represent 50 feet; and through 
the points 2, 3, 4, and 5, draw parallels to AE. These, by 
their iutersections with the lines drawn through A, B, C,&;c., 
will determine the position of the stakes ^j ^? &c. ; and write 
in red ink on the xolot, the height above the plane of reference 
of each stake, taken from the column of total differences in 
the field-book. Let us suppose that- the horizontal planes are 
to be taken at distances of 6 feet. TVe may find the points 
in which the contour lines intersect the lines at right angles, 
as in Example Eirst. If only a rough plot is needed, the 
Surveyor may take the plot thus commenced, into the field, 
and by the eye trace the contour lines on the map. If we note 



216 



ELEMENTS OF SURYEYING. 



[book ni. 



where the lines at right angles, cut fences, roads, streams, &c. 
we can, by joining the points, obtain a plot of the ground. 




30. The contour lines may be traced on the ground, aa 
follows : Set up the level at a, and observe that the back-sight, 
to the stake, placed at (^3), gave a reading of 11.432. Depress 
the yane equal to the distance between the horizontal secant 
planes, that is, 6 feet, which is done by placing it at the reading 
5.432. Then direct the rodman, by signals, up or down the 
hill, till the horizontal hair of the telescope coincides with 
the horizontal line of the vane. The foot of the staff is then 
6 feet above the first point. Let a stake, marked 6, be driven 
here, and direct the rodman around the hill, until a second 
position shall be found, when the horizontal hair of the tele- 
scope will cut the vane, and drive there another stake, marked 
6 ; and so on, until a sufficient number of stakes have been 
driven to determine the curve (6). Then, let the line of stakes, 
marked 6, be surveyed with the compass and chain, and plotted. 
Other contour lines may be found in a similar manner. 



SEC. II.] 



TOPOGRAPHICAL SUEVEYCsG. 



217 



31. When the plane of reference is so chosen that points 
of the work fall on different sides of it, all the references 
on one side are called positive, and those on the other, 
negative. The curves haviug a negative reference are distin- 
guished by placing the minus sign before the number ; 
thus - ( ). 

Shadixo Ais-D Delixeatiox 

32. Figure 7 (PI. 4), represents a piece of ground sloping 
towards D, which is the lowest point; and through this point 
the plane of reference is supposed to pass. The following table 
indicates the heights of the several points above the plane of 
reference. 





Ft. 


Ft. 


Ft. 


Ft. 


c above 


D, 2 


H above D, 7 


2? above D, 9 


B above A 12 


d " 


A 4 


k " A 7 


q " D, 9, 


i: " A 13 


h " 


D, 4 


s " D, 7 


C - A 9 


a " A 14 


t 


A 4 


/ " A 8 


n " A 11 


a « A 15 


9 " 


D, 5 


/ « A 8 


i " A 12 


i^ " A 15 


I 


D,b 


1) ^'' D, 9 
A above j 


m " A 12 

[>, 20 feet. 


^ " A 17 



The first horizontal plane is passed 2 feet above A and the 
curve of intersection with the surface passes through c. The 
second secant plane is passed at 3 feet above D, and intersects 
the surface, in the curve uv, and also near d, which is one foot 
above the curve. All the other secant planes are passed at three 
feet from each other; and, comparing the height of each point 
above D, with the curves lying nearest, on either side, the 
positions of all the points, with respect to the curves, and with 
respect to each other, are easily seen. 

33. The manner of shading the map, so as to indicate the 
hills and slopes, consists in drawing the lines of shading per- 



218 ELEAEENTS OF SUEYEYING. [BOOK IH. 

pendicular to the horizontal curyes, as ah-eady explained. 
These shading lines are drawn close together, when the slope 
is abrupt, and further apart, as it grows more gentle. Fig. 7 
indicates the method of shading. 

34. In topographical surveys, great care should be taken to 
leave some ^:'e?'???fi??e?2^ marlcs, with their levels written on them 
in a durable manner. For example, if there are any rocks, let 
one or more of them be smoothed, and the vertical distance 
from the ^^lane of reference marked thereon : or let the vertical 
distance of a point on some prominent building, be ascertained 
and marked permanently on the building. Such points should 
also be noted on the map, so that a person, although un- 
acquainted with the ground, could by means of the map, go 
upon it, and trace out all the points, together with their differ- 
ences of level. • 

35. Besides representing the contour of the ground, it is 
often necessary to make a map which shall indicate the culti- 
vated field, the woodland, the marsh, and the winding river. 
For this, certain characters, or conventional signs, have been 
agreed upon, as the representatives of things, and when these 
are ouce fixed in the mind, they readily suggest the objects for 
which they stand. Those which are given in Plates 5 and 6, 
have been adopted by the Engineer Department, and are used 
ir all plans and maps made by the United States Engineers. 

It is very desirable that a uniform method of delineation 
should be adopted, and none would seem to be of higher 
authority than that established by the Topographical Bureau. 
It is, therefore, recommended, that the conventional signs 
given in Plates 5 and 6, be carefully studied and uniformly 
followed. 



SEC. m.] RAILWAY CUBYES. 219 

SECTION in. 

RAILWAY CURVES. 

36. Tlie preliminary suiTey of a railroad establishes a suc- 
cession of straight lines, of greater or less length, according to 
the obstacles to be avoided or the advantages to be gained, 
arising from the nature and the contour of the ground. 

The angle formed, at each change in the direction of the 
route, is carefully measured and recorded. 

In the final survey or location, these angles are replaced 
by curves ; and in order that the change in direction shall 
be as gradual as practicable, the straight lines of direction 
are made tangents to the curves at their point of meeting. 

The preliminary survey is termed, by the engineer, *' running 
out tangents." 

37. We will proceed to describe the method of locating 
curves, first giving the mathematical principles applicable to 
the subject. 

Let AD and DB (next fig.) be two tangents, to the arc of 
a circle, AB. Draw the radii AC, BC, and the secant CD. 

The following relations are easily deduced. The tangents 
AD and DB are equal, (Leg., Bk. III., Prob. 14). The angles 
A and B are right angles (Leg., Bk. III., Prop. 9), consequently 
the angles C and D, of the quadrilateral ADBC, must be sup- 
plements of each other. The angle TDB, therefore, must be 
equal to the angle ACB. The right-angled triangles ADC and 
BDC are equal (Leg., Bk. L, Prop. 17); hence, the angle DCA 
is equal to DCB, and each equal to \TDB. 



220 



ELEMENTS OF SURVEYING. 



[book III. 



Let the radius AO he represented by r; the distance AD 
by d, and the angle TDB by a. Then will (Trig., Art. 66), 
d = r tang ^a (1) 

The angle TDB is the angle formed by two straight lines 
of the preliminary survey, and is carefully measured by the 
engineer, in locating tangents. 




From formula (1), we can determine the value of d, for 
any given values of a and r; and hence we can determine, 
at what point on the tangent, laid off from D, the curve of 
any given radius must commence. 

It is evident, both from the diagram and the formula, that 
for any given angle between the tangents, the greater the 
radius of the curve, the greater will be the distance cut off 
between the intersection of the two tangents and the point of 
tangency. 

It is sometimes necessary to give a particular value to d. 
In such case, we use the formula, 

r = d cot ^a ...... (2) 



SEC. III.] EAILWAY CURVES. 221 

38. The work of laying out or locating a curTe in the 
field is somewhat simplified, if the curye have such dimensions 
that one chain, of 100 feet, haye an arc corresponding to an 
exact number of degrees. 

The radii of such curyes are easily calculated. Thus, a 
circle in which one degree of arc measures one chain, will 
haye a circumference of 360 chains, or of 36,000 feet, and con- 
sequently, a radius of o i ^ i ^ = 5729.58 feet. 

In a circle in which two degrees of arc correspond to a 
chain, the radius will be only half as great, or 2864.79. 

When three degrees of arc measure one chain, the radius is 

5729.58 ,Q^QQ. . . 
— - — = 1909.85 feet. 
o 

The number of degrees corresponding to one chain, of a 
railway curve, is called the ^^ degree of curvature" 

The radius of a one-degree curye is 5729.58 feet ; of a two- 
degree curye, 2864.79 feet, &c. 

Eepresenting the degree of curvature by c, we have the 

. 1 5729.58 .^. 

formula, r — (3) 

r being expressed in feet, and c in degrees. 

Apply the preceding formulas (1), (2), (3), to the following 

EXAMPLES. 

1. If the angle TDB, of the tangents, be 45° 10', what dis- 
tance must be laid off from the intersection D, to the point of 
tangency, to admit of a 4° curve ? From formula (3), we have, 

r = — ,— = 1432.39 feet. 
4 

Substituting this value of r in formula (1), we have, 

d = 1432.39 tang 22° 35' = 595.76 feet 



222 



ELEMENTS OF SURYEYING. 



[book m. 



2. If the angle a be 30°, and the distance d be 600 feet, 



what is the radius ? 



Ans, 2239.2 feet. 



3. What is the degree of curvature in the last example ? 
Formula (3) gives 

5729.58 



c = 



= 2.558° = 2° 33' 29". 



4. The angle a being 20° 21', what is the value of d for 



a one-degree curve ? 



Ans. 



The Location of the Cukye. 

39. The location of curves, according to the most common 
method, consists in laying off, at the point of tangency A, such 
angles as shall just subtend one chain of arc. 

If the arcs Av, vw, wx, &c., represent arcs of one chain 
each, the angles ACv, vCio, &c., are each equal to the degree 
of curvature. 




The angles DAv, vAw, ivAx, are each equal to one-half the 
degree of curvature. (Leg., Bk. III., Prop. 1^8.) 

The operations in the field are very simple. The party 
should consist of a transitman, two chainmen, and an axe- 
man. 



SEC. in.] RAILWAY CUBVES. 223 

The transit is set and adjusted at a tangent point, as A, 
and directed along the tangent toward D. 

An angle equal to half the degree of curvature is deflected 
from AD toward the side on which the curve is to run. The 
hind-chainman ho]ds his end of the chain at A. The fore- 
chainman, keeping the chain carefully extended, is directed by 
the transitman into line with the axis of the telescope. This 
locates the point v on the curve. 

From the line Av, another deflection is now made, of the 
same angle as before. The chainmen move forward; the hind- 
chainman stopping at v, while the fore-chainman, keeping the 
chain extended, is directed by the transitman as before, and a 
second stake, w, is fixed on the curve. 

By continuing the process, of deflecting angles equal to half 
the degree of curvature, and causing these angles to subtend 
measured distances of one chain each, the entire curve is 
located. 

The last deflection on the curve rarely corresponds to an 
entire chain; it is, therefore, less than the others. Its amount 
can be readily calculated, when it is remembered that the sum 
of all the deflections, or the angle DAB, is exactly equal to 
one-half the angle a. 

It is sometimes necessary to remove the transit from the 
transit-point to some other point on the curve, before the loca- 
tion has been completed. 

In such a case, the direction of the tangent to this new 
point should be determined. Suppose a; to be a located point 
on the curve to which the transit has been transferred, and 
from which new points beyond x are to be located. Adjust the 
transit and direct the telescope to A. Lay off the angle Axf, 
equal to DAx, (the sum of the deflections made in locating 
Vj w, and x), — xt is the tangent. By revolving the telescope. 



224 ELEMENTS OF SURTEYIXG. [BOOK in. j 

the tangent is produced to 5, from which deflections may be 
made as at first. j 

]N"OTE 1. — The selection of the radius is goyerned by cir- j 
cumstances. Curves of the longest possible radius are, in rail- i 
roads, always the most desirable; but the larger the radius for j 
any particular pair of tangents, the greater the distance by 
which the curve will depart from the intersection of the ; 
tangents. It may happen, therefore, that too large a radius 
may lead to an obstacle, which the angle in the first survey ; 
was made to avoid. i 

The map, therefore, of the preliminary survey, should include | 
so much of the topography of the adjacent section, that the 
radii of the curves may be selected by an inspection of the ' 
map. 

Note 2.— It will be observed that it is the chord, and not ' 
the arc, that is measured for each deflection, when locating 
in the field ; the difference, in railway curves, of proper dimen- > 
sions, does not lead to sensible error. i 

Tor curves of a short radius (less than two thousand feet), 
the error may be diminished, by locating the stakes at half- '; 
chain distances, deflecting, of course, half the calculated deflec- t 
tion angle. | 

LocATio^T OF Curves by the Chai^' aloxe. I 

40. It is sometimes convenient to locate a curve without 
using the transit. In such case, the following method is gen- \ 
erally employed. i 

Let A represent the point of tangency, C the centre, and ; 
V, w, X, located points of the curve, one chain apart. 

From V, draw vti perpendicular to the tangent, and it wiU 
be the first offset, which denote by o. Denote the length of the ' 



SEC. m.] 



EAILWAY CUEYES. 



225 



chain by c, and the radius A C, by r. If, now, we suppose AC 
to be prolonged till it meets the circumference in some point, 
on the other side of the centre C, and this point then to be 
joined with r, and vn then drawn parallel to the tangent, we 
shall have, (Leg., Bk. lY., P. 23), 



Av^ = 2r . An ; hence, o = 



2r- 



(4) 



K, now, we prolong Av, till vt = Av, and join t and w, 
iiu will be the second offset, and will be double vii. For, the 
triangles in the figure, whose vertices are C, and whose bases 
are the equal chords Av^ vw, &c., are isosceles and equal. 




Now, in any one of the triangles, the sum of the two angles 
at the base and the vertical angle C, is equal to two right- 
angles. But, since Avt is a straight line, tv20 + wvC + CvA, 
is also equal to two right-angles. Therefore, tvw \^ equal to 
any one of the equal angles at C, and is, consequently, double 
the angle uAv, which is half the angle C. 

Since the triangle wot is isosceles, if vjp be drawn perpen- 
dicular to the base, it will bisect both the base and the vertical 
angle, making tjp — piu. But the triangles Auv and vtp are 
equal : hence, tw = 2vu. Denoting the second offset by o', we 



have, 



0' = 



(5) 



15 



226 ELEMENTS OF SURVEYING. [BOOK IH. | 

i 
Hence, the practical operation consists in calculating the i 

first offset, which is perpendicular to the tangent, by. formula 
(4), then locating v, on this offset, and at a chain's distance 
from A. 

Having fixed v, prolong Av, and lay off ^^ equal to one chain. 
Then the second, and all subsequent offsets, being double the 
first, we locate w by knowing its distances from v and tj and 
similarly for all other offsets. 

Note. — In employing this method of locating curves, the 
aligning by which the chords are produced should be done with 
much care, as any error in locating a stake, involves much 
greater and increasing errors in succeeding stakes. 

This is called, by engineers, " the method by offsetting from 
tangent and chords produced." 

EXAMPLES. 

1. What are the tangent and chord offsets, for a curve of 
:2000 feet radius; the stakes to be 100 feet apart? 

A71S, From tangent, 2.5 ft.; from chord produced, 5 ft. 

2. Eind offsets for a one-degree curve. 

Ans. Tangent, .87 ft.; chord, 1.74 ft. 



Another chain method, applicable to short curves. 

41. Measure off, on the tangent, 
•any convenient distance, as Aa, 
and offset, at right angles to this 
tangent, the distance a v. If we 
denote the known radius of curva- 
ture by r, the distance measured 
on the tangent from A by d, and 
the offset av, by o, we have the formula, 

= r - Vr' - d' .... (6) 




GEC. m.] RAILWAY CURVES. 227 

Then, by substituting for d in the formula, different dis- 
tances from A, the values of the corresponding offsets are 
found. 

The formula is easily deduced. Foj', draw the radii Cv and 
CA, and vn parallel ,to the tangent Aa, Then, nAav is a rect- 
angle, and in the right-angled triangle Cvn, we have, 
Cv^ = Cn^ + nv-; or, 
'T = {r — oy + d'j from which 
o = r- Vr'-d' (7) 

AxoTHEB Method. 

42. Still another method may be employed in curves where 
the centre is in sight from different points along the tangent. 
It is of use chiefly in staking out circular walks, drives, or 
lake borders in parks. The measurement is made along the 
tangent as in the last case, but the offset is measured directly 
toward the centre by the formula, 

= Vr' + d' -r (8) 

This expression is easily verified. 

examples. 

1. Find the offsets to be made at right angles to the tan- 
gent, at 50, 100, and 150 feet from the tangent point, in a 

curve of 1000 feet radius. 

Am. 1.25, 5.02, and 11.32. 

2. Find the offsets from tangent toward the centime, at 20, 
40, and 60 feet on the tangent ; radius being 200 feet. 

Ans. .99, 3.96, 8.81 (increasing as dr). 

Location of Curves by two Trak'sits. 

43. The surface over which it is necessary to locate a curve, 
may be of such a character as to render it impracticable for the 



228 ELEMENTS OF SURVEYING. [BOOK HI. 

chainmen to make their measurements; if, howeyer, the various 
points are accessible to the axeman, as in the case of marshes, 
shallow lakes, or bays, the stakes may be accurately located by 
the simultaneous deflections of two transits. 

"The method is based on the following geometrical prin- 
ciple : 




Let A and B be the two tangent points of the curve AvB, 
and D the intersection of the tangents. 

If from any point v, on the curve, the lines vA, vB, be drawn, 
then the sum of the angles vAB and vBA is measured by one- 
half the arc AB, and is therefore equal to one-half the angle a, 
or to either of the entire angles A or B, 

To locate the curve in the field, a transit is set at each, of 
the tangent points A and B, and the deflection angle is deter- 
mined as in the first method. 

The transitman at A, deflects in the usual way, one deflec- 
tion angle from the tangent AD. At the same time, the transit- 
man at B defleci;3 the same angle from the chord BA, or what 
amounts to the same, he deflects the difierence between this 
angle and ia, from the tangent BI). The lines of sight of the 
two telescopes now intersect at a point v, on the curve, one chain 
from A. The flagman, directed at the same time by both 
transitmen, is readily brought to the location of the point. 
By a repetitioii of this process the entire curve is located. 



SEC. m.] 



RAILWAY CURVES. 



229 



LAYIlifG OFF THE OrDINATES. 

II. The methods described thus far for locating railway 
curves, applj^ to points 100 feet apart. This is sufficiently 
accurate for the earthwork. In laying the track, however, 
stakes every ten or twelve feet are necessary. These are set by 
drawing the chain or tape in a straight line between the 100-ft. 
stakes, and measuring from it, offsets, as often as desirable, to 
the intermediate points of the curve. 

The length of these offsets, or ordinates, is calculated in 
the following manner: 




ZM 



Let VW represent a 100-ft. chord of a railway curve, of which 
C is the centre. Draw the diameter HK parallel to VW, and 
drop the perpendicular VL. Then, VD = HL X LK, (Legen- 
dre, Bk. IV., Prop. 23, cor. 2). Since IIL = r— 50, and 
LK = r + 50, the value of VL is readily calculated for known 
values of the radius. 

Let N2f be an ordinate, at any distance from VL, say 
10 feet. Then, 

NM' = m£xMK; whence, 
Nj\P ={r- 40) (r + 40). 

Having determined mf, subtract VL from it, and we have 
A7, one of the ordinates required. 

In this manner, by calculating the full ordinate to the 



230 



ELEMENTS OF SURVEYING. 



[book in. 



diameter, and subtracting VL, any desired number of offsets are 
determined for the half chain VF, For FW, the ordinates haye 
the same length, but are located in the inverse order. 

The middle ordinate, FF, is found by subtracting VL from 
the radius. 

EXAMPLE. 

Determined the ordinates 10 feet apart on a 100-foot chord, 
for a two-degree curve. Kadius, 2864.79 feet. 

Ans. At 10 feet . . 
At 20 " . . 
At 30 " . . 
At 40 " . . 
Middle ordinate 





. = 


.15 feet. 




= 


•28 


(( 




= 


.36 


(( 




= 


.42 


a 




— 


.43 


(( 



SECTION lY. 



SECTION LEVELLING. 



45. In the surveys which precede the construction of roads, 
railroads, canals, dikes, or other similar earthworks, the surveyor 
must make such measurements as are necessary to enable him 
to estimate the volume of the material to be removed. In 
addition, therefore, to the horizontal measurements made in 
connection with the location of the work, vertical dimensions, 
or heights, are also necessary, and are taken at every important 
change in the inclination of the surface along the line of the 
survey. 

These heights are taken by the level and rod, and are 
simply vertical distances of points along the surface above an 
assumed level line called the datum line. 



SEC. IV.] SECTION LEVELLING. 231 

46. In the survey of a long line of railway or canal, one 
of whose termini is in the vicinity of tide-water, the datum line 
is usually assumed at the level of mean high-water. In cases 
of surveys entirely inland, the datum line is taken at some 
convenient depth below the beginning point of the survey, and 
at such a distance that it shall be below the entire line on the 
surface. For such surveys, the system of notes described in 
the preceding section is insufficient. 

47. As the survey progresses, fixed points of reference, called 
henclies, are located in the vicinity of the line. Permanent 
objects are usually selected for benches ; such as rocks, build- 
ings, or trees, and at such distances from the line of the work 
as to be undisturbed by the subsequent construction. 

48. Temporary benches, employed merely while changing 
the position of the levelling instrument, are called turning 
2Jomts. In either case, a well-defined point must be provided — 
one not easily disturbed by a blow, and, moreover, one upon 
which the rod can be held vertically. 

l^OTE. — The order of the surveys, on a line of road or canal, 
after the route has been determined by reconnoissance, is 

1st. The Transit survey, establishing the centre line of the 
work. 

2d. The section Level, or the measurement of the profile 
of the centre line. 

3d. The cross-section worh, or the measurements, with the 
level, across the centre line, to the full width of the road, for 
the purpose of determining the intersection of the slo2oes with 
the natural surface; and also, to afibrd data for the estimate 
of the amount of earth to be removed, or filled. 

49. The following example will exhibit the method of re- 
cording the notes of a section level. The datum line is assumed 



232 



ELEMENTS OF SURYETING. 



[BOOK m. 



to be thirty feet below the first bench. When the field-book 
is of the ordinary pocket size, the seven columns of notes will 
generally occupy two opposite pages; the first five being upon 
the left-hand page. 



Beml 



3/. 657 ft above Datum 




Dist. 


+ Sight. 


Ht. of Ins. 


— Sight. 


Surface 
Height. 


Grade 
Height. 


Remarks. 


Bench. 


1 


1.637 


31.637 


2.1 
1.8 


30. . 

29.5 

29.8 




Bench on 

top offence 

-post 30 ft. 

north of 

stake. 


-1 60 






0.9 


30.7 






2 






3.4 


28.2 






3 ' 






10.8 


20.8 






T. P. 


1.910 


22.134 


11.413 


20.224 






4 






5.8 


16.3 






5 






9.0 


13.1 






5^° 






10.4 


11.7 






6 






9.8 


12.3 






7 






10.6 


• 11.5 







The bench having been selected and marked, its location 
is described in the column of remarks. 

The level is adjusted in some convenient place in the vicinity, 
and the reading of the rod is taken upon the bench. In the 
above example it is 1.637. As the bench is 30 feet above the 



SEC. IT.] SECTION LEVELLING. 233 

assumed datum line, the height of the instrument (or line of* 
collimation)- above this datum line is 31.637 feet. 

The reading is recorded against Bench, in the column of 
+ sights, and the '• height of instrument" is recorded in its 
proper column, in the same line. 

By referring to the above diagram it will be readily seen, 
that to obtain the height of the dififerent points 0, 1, 1^", &c., 
above the datum line, it is only necessary to take the readings 
of the rod, at these stations, and subtract them from 31.637. 
Such readings, therefore, are appropriately termed mimis sights, 
and are recorded in the 4th column. As these readings are 
taken only to the nearest tenth of a foot, they are taken much 
more rapidly than the bench readings. The subtractions by 
which the surface heights are found, may be worked in the 
field or not, as the surveyor chooses. The unit of measurement, 
in the column of distances, is usually the engineer's chain of 
100 feet. Readings are taken at intermediate points (as at 160 
feet in the above example) when there are abrupt changes in 
the inclination of the surface. 

50. When it becomes necessary to change the position of 
the level, such measures must be taken as will insure the exact 
" height of instrument," in the new position. 

To effect this, a carefully- selected hard point is found (not 
necessarily on the exact line of the survey, but as far forward 
as convenience and accuracy will permit), and a reading of the 
rod is taken upon it, to thousandths. 

If likely to be used for a single occasion only, it is called a 
^^ turning-point,^^ and marked T. P. in the distance column; 
otherwise it is called a Bench, and its location is described in 
the column of remarks. 

A turning-point is taken between stations 3 and 4, in the 
above example. The reading of the rod, upon it, is 11.413. 



234 ELEMENTS OF SURVEYING. [BOOK IH. 

This is recorded in the — sight column, and the height of the 
point is at once found (by subtracting this reading from Height 
of Instrument), and recorded in the column of "Heights." 

The level is next carried forward to a new position, ad- 
justed, and directed again upon the rod at the turning-point. 
The reading is taken to thousandths. This, when added to the 
height of the turning-point, evidently gives the height of instru- 
ment in its new position. It is recorded, therefore, as a + sight. 
The survey is now continued by taking — sights at the various 
points along the line until it becomes again necessary to change 
the position of the level. 

In the above example, the reading of the rod upon the 
turning-point, from the second position of the level, is 1.910. 
The height of the point upon which the rod stands is 20.224. 
The sum of these, or 22.134, is the "Height of Inst." for the 
second set of — sights. The successive subtractions of the 
readings from the Height of Instrument, give the surface heights 
as before. 

The most extended section levels are but repetitions of this 
process. 

The rules for taking and recording field-notes in section 
levelling are as follows: 

I. The " distances'^ recorded in the first column are the hori- 
zontal measurements, in chains, from the leginning of the survey 
to the points luhose heights are to he determined. The heights 
are taken at each ivhole chain, and at such intermediate points 
as the irregularities of the surface require. 

II. The first reading of the rod, after each setting of tlie 
level, is upon a lench or turning-point, and is . « " + sight :" 
all other readings are " — sights." 

III. Tlie -^ sight, added to the height of the point upon 
which the reading was taken, gives the ''Height of Instrument." 



SEC. IV.] SECTION LEVELLING. 235 

IV. The — sights taken, at any position of the level, sub- 
tracted from the ^^ Height of InstrumenV^ for that position, give 
the corresponding ^^ Surf ace Heights" 

V. All the + SIGHT readings, and the last — sight of each 
set, being upon benches or turning-points, are talcen to thousandths 
of a foot. The remaining " — sights" are talcen to tenths only, 

ISToTE. — It will be observed that when the column of " surface 
heights" is complete, the second, third, and fourth columns of 
the field-notes are no longer needed. The first and fifth columns, 
which together contain the horizontal and vertical measurements 
for the line of work, afford all the data necessary for mapping 
the profile and determining the grade-line. 

The location of the benches should be so described in the 
column of "remarks," that any particular bench may be found 
at any time, by referring to the field-notes. The importance 
of this is apparent when it is remembered that the process of 
construction destroys or removes the stakes along the line of 
the survey, and that the question of the completion of the work 
can be determined only by reference to the benches. It is 
obvious, also, that they should be established somewhat off the 
line of the survey. The distance apart, of regularly established 
benches, should be governed by the above-mentioned uses of 
them. 

Any turning-point may be profitably made a bench (when 
it can be made permanent), by carefully recording, so as to 
admit of its identification. 

In conducting a section level through a rocky district, turn- 
ing-points in abundance are found at hand, and cause no delay 
in their preparation, whereas a bench in the same section, re- 
quires marking and locating. 

In levelling through flat and level sections of country, 
although the engineer can get "sights" for long distances, a 



236 ELEMENTS OF SUKYEYING. [BOOK HI. 

proioer regard for accuracy will induce him to limit the distance, 
between successive positions of the level, to about six hundred 
feet. Under such circumstances, each turning-point is made a 
bench. 

51. The methods of establishing benches are various. In a 
rocky section, some conspicuous point is marked either by 
drilling or grooving the rock. In villages or cities, stone steps, 
or projecting courses of masonry to dwellings, curb-stones, and 
fence-posts afford good benches, and admit of easy identi- 
fication. 

In sections where trees abound, a notch is cut in the side 
of a trunk near the root, in such a manner as to leave a pro- 
jecting point upon which the rod may be held vertically. A nail 
driven full length into the projection, gives it the necessary firm- 
ness for a bench. 

In marshes or prairies, where there are neither rocks nor 
trees, the engineer is compelled to resort to long stakes, firmly 
driven into the ground to such a depth as to be undisturbed by 
.the frost; no portion of the stakes being allowed to project above 
the surface. The top of each is trimmed to a kind of blunt 
point, into which a nail is driven its full length. 

A re-survey of a route, to detect possible errors in levelling, 
is accomplished by taking the heights of the "benches" only, 
and is called a "cheek level." 

Deatving the Peofile. 

52. When the "section level" of a line of work has been 
completed, the "profile" is next to be drawn. The method of 
doing this is very simple. 

A horizontal line to represent the datum line, is first drawn, 
and the distances from the first column of notes are laid off 



SEC. IT.] SECTION LEVELLING. 237 

along it, to a convenient scale : this for ordinary working draw- 
ings is about two hundred feet to an inch. 

The "surface heights" corresponding to these distances are 
next laid off at right angles to the datum line, and above it, 
but to a scale usually ten times as great as that employed for 
the horizontal distances ; that is, an inch upon the vertical lines 
represents one-tenth as many feet as upon the datum line. A 
line joining the upper extremity of the verticals, is the profile. 

By thus employing two different scales, the irregularities 
of the surface are made more apparent to the eye, and the sub- 
sequent adjustment of the "grade-line" is rendered much easier, 
and more accurate. 

53. Every earthwork of importance requires, in addition to 
the working profiles, a general map, in which the plan drawn 
from the transit survey is represented upon the same sheet as 
the profile. 

The horizontal distances of both portions of the map being 
drawn to the same scale, and one being placed directly above 
the other, corresponding points in plan and profile are readily 
compared. 

In published maps of this kind, representing extended works, 
and drawn for convenience to a very small scale, the vertical 
scale of the profile is frequently several hundred times as great 
as the horizontal. 

Establishment op the Gkade. 

54. The determination of the height which the finished road 
or canal, shall have above the datum line at different points, is 
called "Establishing the grade." 

The position and inclination of grade-lines are influenced 
by a variety of circumstances: 



238 ELEMENTS OF SURYEYING. [BOOK HI. 

1st. The chanictcr of the work. A street admits of an in- 
clination of fiye, or eyen eight feet in a hundred, and requires 
about one foot for its drainage, while a rise of two feet in a 
hundred upon a railroad is exceedingly rare. A canal is, of 
course, level, the change of height being effected ' by abrupt 
transitions at the locks. 

2d. The economy of construction. It is desirable to make 
the earth excavated, form the required embankments, or, in 
the language of the engineer, "to make the cuttings balance 
the fillings." 

It is, however, sometimes more economical to throw away, 
or "make a spoil bank" of the earth of an excavation, than 
to transport it the required distance for the embankment. 
Embankments, for similar reasons, are often constructed of 
earth obtained outside of the road limits (" borrowing pits") ; 
or, when such means are not available, are often made of timber 
framing, (trestle-work). 

3d. The natural obstacles, which render the construction 
difficult; such as rocky ledges, marshes, lakes, streams, and 
quicksands. 

In either case, the engineer determines, by inspection of 
the maps, at what points the grade-line shall intersect the 
natural surface. Thus the inclination of the grade, and, con- 
sequently, its height above the datum line, for each " distance," 
are easily found. 

Another column of notes is now made, recording these 
" Grade Heights ;" each being placed against the corresponding 
surface lieiglit. 

The following example, with its accompanying diagram, 
illustrates the method of establishing a grade and recording 
the notes. It will be .observed that the profile, with its "dis- 
tances" and "' surface heights," are the same as in the preceding 
problem. 



SEC. lY.] 



SECTION LEVELLING. 



239 



"We will suppose it is required to establish, in tlie following 
profile., a grade-line wliose inclination shall not exceed 3 in 100 ; 
the grade to begin at station 0, at the surface. 



260 




. Dist. 


.s. 


H. of Ins. 


— S. 


H.ofSur. 


H.ofGr. 


Cut. 


Fill. 


RE3I. 











29.5 


29.5 








1 








29.8 


26.8 


3.0 






160 








30.7 


25.2 


5.5 






2 








28.2 


24.1 


4.1 




at 2" 


3 








20.8 


21.4 




0.5 




T.P. 


















4 








16.3 


18.7 




2.4 




5 








13.1 


16.0 




2.9 




5" 








11.7 


14.7 




3.0 




6 








12.3 


13.3 




1.0 




7 








11.5 








at 6" 



It is an easy matter to represent any required inclination 
of grade on the profile map ; nothing more being necessary 
than to lay off the proper distances on two different yerticals, 
and draw a line through the points of measurement. For in- 
stance : a grade of 3 in 100, running downward from station 0, 



240 ELEMENTS OF SURVEYING. [BOOK in. 

would intersect the vertical at 6, eighteen feet lower, and the 
vertical at 7, twenty-one feet lower. 

Moreover, by. consulting the notes, we find that a grade- 
line from 0, whose height is 29.5 feet, ending at the surface 
at 7, whose height is 11.5 feet, descends 18 feet in 700, or 
2.57 in 100. 

Either of these lines would fulfil the required conditions. 
The first w^ould, however, require in its construction a large 
excess of excavation over the embankment (as may be seen by 
drawing a faint line in the diagram). The second would give 
an excess of embankment. 

It is best, generally, that the cutting should be slightly in 
excess, as nearly all kinds of earth shrink a little in the pro- 
cess of removal. 

The cuttings and fillings of the profile may be balanced 
with tolerable accuracy, by stretching a thread across the pro- 
file so as to intersect at the point, and then varying the in- 
clination, until the areas cut off by the profile line on oppo- 
site sides of the thread appear equal.* 

The column of Grade Heights must now be filled. It is 
easily and rapidly done. The height of Grade, at 0, is, by the 
conditions, 29.5. At station 1, it must be 2.7 lower, or 26.8; at 
1.60, 4.3 lower, or 25.2 ; and at 2, 5.4 lower, or 24.1, &c. 

The remaining columns of '"cut" and "fill" contain simply 
the differences between corresponding "surface" and "grade 
heights." Where the surface is higher than the grade-line, the 
construction requires a "cutting;" when the established grade- 



* The advantage of a thread over a ruler lie? in thfe fact, that while using the thread, 
the areas on both sides of it are seen at once. 

In the present example, a line from 0, descending 2.7 to 100, seem? to accomplish the 
desired purpose. The line being drawn, the '"cut" and "fiU" areas are measured, to deter- 
mine if they are properly balanced. 

The complete computation of the earthwork, by which the exact position of the grade- 
line is determined, is explained in the next section. 



SEC. IV.] SECTION LEYELLING. 241 

line is higlier than the surface, an embankment, or "filling," is 
necessary. 

The notes in the final column, indicate the points where the 
grade-line intersects the natural surface. Such are called zero 
points. 

The distances are of importance in the computation of the 
earthwork. The above notes literally signify that either cut or 
fill is 0, at 2.87, also at 6.52. 

"^These distances are obtained with sufficient accuracy for 
ordinary purposes by a measurement of the profile map. When 
the cuttings and fillings are recorded in the proper columns,, 
the notes belonging to the section-level are complete.* 

Note. — It will be observed that the first set of notes on 
page 232, did not contain the columns for cut and fill. 

The practice in keeping the notes differs with the work to 
be performed. 

In extensive railway surveys, it is convenient to rule the 
pages of the note-book as in the first example ; carrying out the 
field-notes to the extent of the surface heights, at least; then 
transfer to another book, the " distances," " surface heights," and 
"grade heights," ruling columns for "cut," "fill," and "remarks." 

These transferred notes tve recorded in ink, and reserved for 
use in mapping and computations. 



♦ The following calculation may be employed in the more important cases. The 
triangles formed by the verticals (cut or fill), the grade-line, and the Burface-line are 
similar, and give the following proportion : 

The sum of the cut and fill, 

: the cut, 
: ; the distance from cut to fill, 
: distance from the cut to point. 
Fill may be substituted for cut in the second and fourth terms. 
The application to the first zero point, in the above notes, is as follows: 

4.1 + 0.6 : 4.1 : : 100 : required dist., or 87. 
In the second case in the notes, the cut necessary to the calculation is wanting, but 
is easily suprjlied, by determining the height of grade in the usual way at station 7. 

16 



242 



ELEMENTS OF SURVEYING. 



[book m. 



Most road or canal surveys are made on several trial-lines 
before one is finally adopted. The profile of each line is care- 
fully drawn, and the cost of construction approximately esti- 
mated. 

When the route is finally selected, and the section levels 
satisfactorily completed, the exact width of the earthwork, both 
in excavations and embankments, is carefully staked out and 
the amount of material to be moved in the progress of construc- 
tion, accurately measured. 

The method of conducting this work is explained in the 
next section. 

Before closing the subject of section levelling, we will con- 
sider the profile represented in the figure, and the set of field- 



70.942 




notes appended, which are only partially completed, and which 
will afibrd some examples for practice. 



SEC. IT.] 



SECTION LEVELLING. 



243 



Dist. 


+ s. 


Ht. of Ins. 


-S. 


Surface 
Heights. 


Eemarks. 


Bench. 


1.032 

















3.2 






1 






3.8 






2 






5.3 






3 






8.9 






350 






10.3 






4 






9.0 






5 






4.8 






T.P. 


11.815 




2.346 






T.P. 


10.942 




2.318 






6 






9.7 






6" 






6.4 






7 






2.1 







1. What is the 
of the level ? 

2. What is the 

3. What is the 
level ? 

4. What is the 

5. What is the 
level ? 

6. What is the 



9. 


(( 


n 




10. 


(( 


a 




11. 


Write 


the 


(( 


and 6". 







" Height of Instrument" for the first position 

A71S. 31.032. 
height of the first T. P.? A7is. 28.686. 
" Ht. of Inst." for the second position of the 

Ans, 40.501. 
height of the second T. P. ? Ans. 38.183. 
" Ht. of Inst." for the third position of the 

Ans. 49.125. 
Height of Surface at ? 
at 3 ? 
at 3^° ? 
at 5 ? 
" " at 6 ? 

at 7 ? 
Surface Heights" for the distances 1, 2, 4, 



71S. 


27.8. 




22.1. 




20.7. 




26.2. 




39.4. 




47.0. 



2M 



ELEMENTS OP SURYEYING. 



[book III. 



Ceoss-Section" Levellin^g. 

55. All earthworks, whether excavatiou or embankment, un- 
less held in position by retaining walls, require to be constructed 
with a sloping surface, the inclination of which depends upon 
the kind of earth. 

If, in a railway- cutting, for instance, the banks which bound 
it be left too nearly vertical, when first constructed, the weather- 
ing influences, to which they are subjected, soon cause the ma- 
terial to slide down, until the whole slope gradually assumes a 
much lower inclination. 

After a time, however, the tendency to roll or slide is checked 
by the friction of the particles themselves, and the slope thus 
formed will withstand the ordinary effects of sun, wind, and 
rain. The inclination thus assumed is called the "natural slope" 
of that kind of earth.* 

Slopes are expressed mathematically by the ratio of their 
horizontal to their vertical dimensions, and which is called the 
ratio of slope. 




In the diagram, which represents a road-cutting, the ratio 
of ES to AE, or of FS' to BF, is the ratio of slope. 

In practice, the slope at which earthworks are allowed to 
stand, vary from 1 to 1, or 45°, (as in very coarse material) ; to 
2 to 1, or 26° 34', in very fine sand. 



* This slope is determined, experimentally, "by dryino; a portion of the earth, and 
then pouring it from a slight elevation upon a level surface. The heap thus formed 
is a rather flat cone, whose sides stand at the lowest inclination they would he liable to 
assume under the action of atmospheric influences. The angle with the horizontal plane 
will be somewhere between 25° and 45°. 



SEC. IV.] 



CROSS-SECTION LEVELLING. 



245 



A elope of H to 1, (33° 41'), is found to be so far suitable 
for all ordinary excavations or embankments, that it is common, 
in the absence of an examination of the material, to adopt it 
as the ratio of slope throughout. 

SETTii^^G Slope Stakes. 

56. It is evident that the width of natural surface of ground, 
required in the construction of a road, will vary with the depth 
of excavation or embankment. 

As often, therefore, as it is found necessary to determine 
the depth of the cutting or filling, in the section level, it is 
also necessary to mark the boundaries of the width of the 
work, on the natural surface. This is done by stakes called 
Slope StaJces, and the field-work necessary to determine their 
position, and to measure the section taken across the road, of 
which the Slope Stakes indicate the boundaries, is called " Cross- 
Section Levelling," or " Cross-Section Work." 

57. A party of five may be usefully employed in setting 
Slope Stakes; viz., a leveller, rodman, axeman, and two tape- 
men. 

The rod, for Cross-Section work, is a ruder instrument than 
that employed in the Section level. It should be at least fifteen 
feet long, with the feet and tenths plainly marked. It requires 
no target, the leveller himself reading the rod in the act of 
sighting. 

The field-book is ruled as shown below. 



Diet. 


Left. 


Centre 
cuttings. 


Eight. 











246 



ELEMENTS OF SURVEYING. 



[book m. 



The left-hand column contains the distances taken from 
the Section-level notes. The third column is for the cut or 
fill, corresponding to the distance in the first column; these 
numbers also being taken from the notes of the section level. 

A filling, it should be remarked here, is designated as a 
minus cutting in the field-notes. 

The second and fourth columns are for the horizontal and 
vertical measurements of the cross section. 

The examples following will illustrate the method of meas- 
uring the section and recording the notes. 

Let figure represent a section across a road excavation. AB 
being the bed of the road, and 8CS' the line of the natural 
surface. 

The road-bed is supposed to be 16 feet w^de, the centre 
cutting 12.4 feet, and the ratio of slope 1^ to 1. 




The level being set up and adjusted in a convenient place, 
the rod is first held by the centre stake at C, and a reading 
taken. 

In the present example, the reading is 5.4. The line AB 
forms a convenient datum line, and the height of the instru- 
ment above this line, is evidently 12.4 + 5.4 = 17.8 ft. 

This is noted down, for the moment, on a reserved page 
of the note-book, or on a spare slip of paper; neither the height 



SEC. IT.] CROSS-SECTION LEYELLING. 247 

of instrument or rod readings being matters of permanent record 
in cross-section work. 

It is evident that if the rod be held at different points along 
the surface, and the readings subtracted from the "height of 
instrument," the remainders will be the heights of these points 
above the datum line AB. These heights are technically called 
cuttings, although in the case of ST and S' V, no actual excava- 
tion is proposed. 

The reading at B is supposed to be 5.5. The cut is therefore 
12.3. The horizontal distance from the centre is 8 feet. For 
each cutting there will be a horizontal measurement, and these 
two must be recorded together. 

The form adopted is that of a fraction in which the numera- 
tor is the cutting and the denominator the distance. 

The record of this measurement would be, therefore, -^^, 
in the column marked "left." The points A and B, of the 
cross section are appropriately termed the angles, and as the 
points F and F, directly over them, become new starting-points 
for horizontal measurements, it is important to distinguish them, 
in some way, in the notes. 

(Right and left in the actual survey are determined by the 
direction in which the survey progresses, and in which the 
centre stakes are numbered.) 

A common method is the one adopted in our notes — to sub- 
stitute for the number which represents the half width of the 
road, the letter A. 

The hind-chainman now takes his position at F, and 
the remaining distances to the left are measured from this 
point. 

A change in the surface-line at H requires notice. The 
reading of the rod 6.2 indicates a cut of 11.6. This, with the 
distance from F, 10 feet, is duly recorded. 



248 ELEMENTS OF SURYEYING. [BOOK IH. 

There being no other material change in the surface line 
beyond //, there remains to be determined on this side only the 
intersection S, of the surface and slope. 

It is found by trial. When found, it is evident that the 
ratio of the distance to the " cut," must be the same as the ratio 
of slope. In the present example, the distance must be 1^ times 
the cut. 

Suppose a trial reading taken at 25 feet, out, is 3.2. The 
height, or cut, is (17.8 - 3.2) r^ US. 1^ times this" is only 21.9 
feet. The distance tried, 25 feet, is too great. 

Suppose a second trial at 22 feet out, with a rod reading 
of 3.8. The cut is 14. 1|- times this is 21. Still too far out 

A third trial, at 21 feet out, and a reading of 4, gives a cut 
of 13.8 ft. This mnltiplied by 1^ gives 20.7 feet. The measured 
distance is slightly too great, but in ordinary practice this ap- 
proximation -would be considered near enough. The record for 
the slope-stake S would therefore be if;f .* 

In proceeding from the centre to the right, we find a point 
K between the centre and the angle, that requires attention. 

The distance in such a case is taken from the centre instead 
of the angle. CK is 3 ft. and the rod reading 5.3 gives a cut of 
12.5. The reading at the angle-stake F is 5.8, giving a cut 
of 12 feet. 

If the surface-line from F were level, the distance FS' would 
be 12 X li = 18 feet ; but as the ground descends, the distance 
is less. 

A trial at 11 ft. with a reading of the rod of 10.4, indicates a 
cut of 7.4. This multiplied by 1^ gives 11.1, which is very nearly 
right: -j^^y is therefore the record for the location of S'. 



* The readings and distances in this example have heen made to correspond to a 
rise of one foot in five from H to S. The exact record for S is 2 u:i:f • 



SEC. B\] CROSS-SECTION LEVELLING. 249 

The completed notes for this cross section are as follows: 



Dist. 


Left. 


Centre Cut. 


Eight. 




13.8 

20.7 


11.6 
10 


12.3 
A" 


12.4 


12.5 
3 


12 
A 


7.4 
11.1 





58. We wiU now give a similar example, illustrating the 



method of staking out embankments. 




us 



Dist. 


Left. 


Centre Cut. 


Pdght. 




- 15.8 - 12.8 
23.7 A 


-11.7 


- 8.6 - 8.4 
A 12.6 





The filling at the centre is assumed to be 11.7 ft., which 
appears in the column of "centre cut," with its appropriate 
sign. 

The reading of the rod, at the centre, as shown by the dia- 
gram, is 7.2. 

The sum of the reading and the centre cut, (7.2 — 11.7), 
is — 4.5, which is the ''height of instrument" referred to the 
line AB. 

The readings at all other points along the line SS', must 
be subtracted from this "height of instrument," as in the pre- 



250 ELEMENTS OF SURVEYING. [BOOK IH. 

ceding example. The several remainders are the corresponding 
" cuttings." 

The reading • at angle stake E, 8.3, subtracted from — 4.5, 
gives — 12.8, for the cut. 

For the slope stake S, we will suppose a trial distance of 20 
feet from E, and a rod reading at the trial point *of 10.8 feet. 
The cut is therefore, — 15.3; this multiplied by IJ gives 
22.95.* The trial distance therefore, 20 feet, is not enough. 

A trial of 24 feet out, we will suppose to give a rod reading 
of 11.3 ft, which corresponds to a cut of — 15.8 ft. The ratio 
applied to this, gives for the proper corresponding distance out, 
23.7 ft., which is nearly correct. The distance at which the trial 
was made is slightly too great. It is evident that if the slope 

stake be set at the calculated distance, 23.7 ft., the record of 

X5 8 

^ may be made without involving an error of more than 

/vd.7 

a tenth of a foot, in either cut or distance. 

On the right, the reading at the angle stake F, is 4.1. The 
cut, therefore, is — 8.6 feet. 

As the surface rises but little from F to 8', the trial distance 
for the slope stake is taken at 12 feet ; (it should be 12.9 ft., if 
the surface were level): the reading is supposed to be 3.9 feet. 
This gives the cut — 8.4, which should correspond to a distance 
out of 12.6 feet. It is evident, that considering the rise in the 
surface and the rod readings at F and ;S", the rod reading at S' 
would not vary a tenth if moved from 12 feet to 12.6. The 

^.4 



record, therefore, for S' is 



12.6 



50. The rules for conducting and recording cross-section 
work, whether for excavation or embankment, are as follows: 

I. Prepare the field-looh lij ruling columns for Distances 

* The sign is disregarded in the product. It may be well to notice, however, that the 
ratio of slope in embankments is considered to be li to — 1. 



SEC. IT. J CROSS-SECTION LEVELLING. 251 

and Centre Cuttings, leaving u'ider spaces on either side of the 
latter column for the record of the various ineasurements to the 
left and right of the centre stake. Transfer from the section- 
level 7iotes the distances and corresponding cut or Jill, for each 
stake of that survey. Filling in the cross-section notes is desig- 
nated as minus cutting. 

II. Having set the level in convenient proximity to a pro- 
posed cross section, take a reading of the rod at the centre stake. 
Add this reading to the centre cutting, (regarding the sign of 
the latter), to oltain the *' height of instrument.'^ 

III. Lay off half the width of the road-led each side of the 
centre, and mark the distances, temporarily, luith stakes. TJiese 
are the angle stakes. 

IT. Proceed to take rod readings at the angle stakes, and 
beyond them, outward, (on a line at right angles to the direction 
of the line of the road), at each change of inclination of the 
surface. Subtract each reading from the height of iiistrument ; 

the remainder is the cutting, or vertical distance of the point 
measured, from the proposed road-bed. 

Y. Record each cutting, together ivith its horizontal distance 
from the nearest angle stake, in the form of a fraction express- 
ing the ratio of the distance to the cutting. Each fraction being 
recorded in its proper column either ^'righf' or "left;' of the 
centre. Points between the centre and angle stake, are located 
by measuremetits from the centre. 

VI. To find the position of the slope stake : Measure off a 
trial distance from the angle stake, and determine the cut as 
before. Multiply the cut by the ratio of height to base of the 
proposed slope. If the trial distance be greater than this product, 
the assumed point is too far out, and vice versa. Repeat the 



252 



ELEMENTS OF SURYEYING. 



[book m. 



trial tintil the ratio of the distance to the cut expresses the ' 

ratio of slope. \ 

1 

60. The cutting at the angle stake is, in cases of a tolerably ; 

uniform surface, a good guide to the distance to the slope i 

stake. Thus, when the angle cutting of an excavation is 16 , 

feet and the ratio of slope 1^ to 1, the distance out, for a level , 

1 
surface, would be 24 feet; but if the ground in that distance 

rise 2 feet, (and which in practice may be determined pretty ' 
correctly by the eye), then the horizontal distance must be in- 
creased by something more than 1|- times 2 feet. ] 
When the surface descends, the estimated distance out, for | 
a level surface, should in like manner be diminished. In em- I 
bankments the conditions are reversed; the steeper the rise, the 

'i 

shorter the distance out. j 

I 

61. The following examples will serve to elucidate the sub- ! 

ject still further. 




Dist. 


Left. 


Centre 
Cut. 


Eight. 




- 4. - 4.5 
6. A 


-4.9 


-6.1 
A 


-6.4 
4 


- 7.4 
11.1 





The diagram represents an embankment cross section, in 
which, by reason of the small depth of filling, the height of 
instrument is a positive quantity. 



SEC. IV.] 



CROSS-SECTION LEYELIilNG. 



253 



The centre cut is —4.9; reading of the rod at the centre, 
8.5 ; the sum of these, or " height of instrument/' is 3.6. The 
remaining rod readings are given on the line through the in- 
strument. . 

62. In the example of the following diagram, the cross 
section is partly in excavation and partly in embankment. The 
ratio of slope is 2 to 1. The centre cut is 2.4. The centre 
reading is 7.9; height of instrument, 10.3. 

The reading at H, is 6.3 ; at E, 6.1 ; at 8, 5.4. The point, 
K, is efjsily found in practice, it being that point on the surface- 
line where the reading of the rod exactly equals the height 
of instrument. The reading at F is 13.2 ; and at ;iS^', 15.8. 

From these readings the cuttings may be found, and the 
notes completed as below. 




Dist. 


Left. 


Centre 
Cut. 


Right. 




4.9 4.2 4.0 
9.8 A 3.8 


2.4 


- 2.9 - 5.5 
.4 A 11 . 





63. In the following example, there is a regular rise in the 
surface-line of one foot in eight. The ratio of slope in the 
excavation is to be IJ to 1 ; height of instrument, 14.2. 

In seeking for the position of the slope-stake S', a distance 

23 



254 



ELEMENTS OF SURVEYING. 



[book in. 



out of 13 feet is tried; the reading of the rod at the trial 
point is 4.8. 




How does this point compare with the true position of S' ? 

Ans. Not far enough out. 
What is the result of a trial at 16 feet out and a reading 
of 4.4? Ans. Too far out. 

9.6 
14.4 

4.9 



What is the true cut and distance at S' ? Ans, 



Find the position of ^S'. 



Ans. 



7.3 



Note 1. — It sometimes happens, in yery hilly sections, that 
it is impracticable to sight to all the necessary points of a 
single cross section from one position of the leyel. In such 
a case, it is only necessary to work from the centre as far as 
the surface will permit, then establish a turning-point, precisely 
as in section levelling; change the position of the level so as 
to proceed with the work, and determine the new height of 
instrument, from which the readings are to be subtracted as 
before. 

Note 2. — The degree of accuracy desirable to be attained 
in setting the slope stake, varies with the kind of earth to be 
" staked out," so that no exact rule can be laid down. 

A principle, in quite general use, permits the stake to be 
set when the calculated distance varies from the trial distance 
by less than a foot. 

The limit of error should never be greater than this, but 
in rock and the harder kinds of earthwork, it should be made 
much less. 



sec. iv.] cross-section levelling. 255 

Computation of Eaethwork. 

64. Before the work of construction of a railroad or canal 
commences, the calculation of the earthwork must be com- 
pleted. 

The cross-section levels afford the necessary data. These 
surveys have divided the proposed work into blocks of 100 feet, 
or less, in length, and which are appropriately termed prismoids. 
Different methods are employed for estimating their cubic con- 
tents. The most accurate, though the most laborious, is the 
prismoidal formula, (Leg., Mensuration, page 129), 

vol. = ^ (B + B' + 4J/) 

B and B' representing the areas of the end sections of the 
prismoid, 31 the area of a section midway between them, and 
I the entire length of the solid. 

The principal difficulty in applying this formula lies in 
finding the dimensions of the middle section. 

^Ye will show the application of the formula by an example 
of road excavation. 

To simplify the problem, we will suppose such a degree 
of regularity in the ground surface that the angle cuttings 
may be omitted. 

The length is supposed to be 100 feet. The other dimen- 
sions are given in the diagram. 

The areas of the end sections are easily found. It is only 
necessary, in each case, to add together the areas of the trape- 
zoids composing the whole end figure, as represented in the 
diagi'am, and subtract therefrom the sum of the triangles which 
lie outside the section. The dimensions of these triangles are 
always expressed in the cross-section notes, by the records for 
the slope stakes. 



256 



ELEMENTS OF SUKYEYING. 



[book III. 



The area of B is thus found to be 104.8 sq. feet, and of B', 
116 sq. feet. 



7.2 




\2.6 M 



Now, if a section of this prismoid be taken midway between 
the two ends, each of its several dimensions must be an arith- 
metical mean of the corresponding measurements of the end 
sections. Thus, the centre cutting is found to be 5 ft. ; the dis- 
tance from the angle to slope stake, on the left, 9.9 ft, f — '-- J ; 

the cutting on the extreme left is 6.6 ft, f -^^—^ — j &c. 

The area of 31 is 111.3 sq. ft 

Vol. of the prismoid = ^ X 100 (104.8 + 116 + 445.2), 
= 11100 cubic feet 



65. Two other methods of computation are of frequent use 
among engineers. They are less laborious than the prismoidal 
rule, but they are also less accurate. 



SEC. lY.] CROSS-SECTION LEVELLING. 257 

The first is known as the "Arithmetical Average" method. 
The rule is : 

Multiply half tlie sum of the end areas hj the length of the 
jprismoid. 

Applied to the example just solved, we should have, 
Tol. = 100 X ^°^-^ + "'^- = 11040 cu. ft. 

66. The other method is called the " Mean Average" method. 
The rule is expressed thus : 

Add together the two end areas and their geometrical mean 
proportional. Multiply this sum hy one-third of the lengtli of 
tlie prismoid. 

This method, applied to the example, gives for the volume: 

vol. = -i X 100 (104.8 + 116 +\/l04.8x 116) 
o 

= 11035 cubic feet. 

Note. — "When the difference between the end areas is con- 
siderable, the mean aVerage method gives better results than 
the method of arithmetical average. 

The last mentioned rule has been largely employed by the 
engineers of the public works of the State of ISTew York. 

Tables based upon the prismoidal formula, or modifications 
of it, are much used by engineers in earthwork computations. 

67. In applying the prismoidal formula to an example in 
which one end section has more given dimensions than the other, 
the calculator is frequently in doubt how he shall average these 
dimensions to obtain the middle section. As a rule, each cut- 
ting of the most irregular section should be averaged with the 

cutting nearest opposite to it, in the other section. 

17 



258 



ELEMENTS OF SURVEYING. 



[book III. 



We will illustrate this by a final example of earthwork : rep- 
resenting tlie sections by the field-notes only. 



Dist. 


Left. 


Centre 
cut. 


Right. 


2 
2.60 


17.2 
25.8 
11.6 
17.4 


16.8 

A 

11.2 

A 


16 

2 


15.8 
10.4 


13 

A 

10 
A 


10 8.4 
8 12.6 

8 

12 

1 



The half-width of the road, for which A is given in the notes, 
is to be considered as 8 feet. The length of the prismoid is 
'expressed by the difference of the given distances, or 60 feet. 

The dimensions of the middle section are found as follows: 

The centre cut is half the sum of the given similar dimen- 
15.8 + 10.4 



■sions. 



2 



13.1 feet. 



11.5 
On the right, the average of the angle cuttings gives — r^ ; 

A. 

for the next measurement, both cut and distance must be aver- 

:aged 'y it is, 

i.X(10 + 8) = 9 _9_ 

iX (8 + 12) = 10 ^^' 10' 

The last term in the upper section must be averaged with 
the last in the lower, thus: 

iX ( 8+ 8.4)= 8.2 8.2 

or • • 

iX (12 + 12.6) = 12.3 ' 12.3 

-I n 

On the left, the measurement — of the upper section, must 

be averaged with the centre cutting of the lower, being nearest 
opposite to that point. We have, 

^ }X (16 + 10.4) = 13.2 m 

iX( 2+ )= 1 ^"^^ 1 



SEC. v.] MINING SURYEYING. 



259 



14 
At the angle, in like manner, we have -^ ; and finally at 

14 4 
the slope stake ^. The complete dimensions being 



21.6 

d. 1 ^9. I 

13.1 



14.4 14 13.2 
21.6 A 1 



11.5 9 8.2 
A 10 12.3* 



The area of the upper section, after subtracting the tri- 
angles, as before, is 543.47 sq. feet. 
The area of the lower end section is 325.44 
The middle section contains 429.8 sq. feet. 
The Yolume of the prismoid is 

1 X 60(543.47 + 325.44 + 4 X 429.8) 
=25881.1 cubic feet, or 958.56 cubic yards. 



SECTION V. 

MINING SURVEYING. 
Definitions and general Notions. 



68. Mining Surveying comprises all the operations neces- 
sary to determine the relative positions of the parts of a mine 
with respect to each other, and also, with respect to the surface 
of the earth. 

69. The general principles involved in this branch of sur- 
veying are the same as those used in surface surveying, but, 
from the nature of the case, certain modifications are required, 
both in the instruments employed and in the manner of using 
them. 

Stations are designated by lamps instead of flags, and lamp- 



260 ELEMENTS OF SUKYEYING. [BOOK IH. 

stands instead of flag-rods ; station points, if temporary, are 
marked by cross lines chipped in the rock, or sometimes by 
simple chalk lines, and, if permanent, by iron pegs driven into 
holes drilled for the purpose. Lines are measured along the 
slope, instead of on the horizontal, the chainmen being guided 
by lamps instead of rods. Angles are measured by instruments 
specially devised for underground use ; the comjmss, when used, 
is generally of a widely different form from the ordinary sur- 
vey or's compass; the theodolite, which is the principal angular 
instrument employed, differs from the ordinary theodolite in 
having a diagonal eye-piece, to permit observations to be made 
when the telescope is directed vertically upward, and also an 
arrangement for illuminating the cross hairs. These modifica- 
tions will be more fully described in a subsequent article. 

Traversing. 

70. Teayersixg is the operation of running a zig-zag line, 
from one point to another. The elements of the traverse are 
straight lines, determined by their lengths and by their in- 
clinations to certain fixed planes. In mining surveying, three 
such planes are used; the first, is either a meridian plane 
through the origin- of the traverse, or a vertical plane through 
the first course ; the second, is a horizontal plane through the 
origin ; and the tliird, is a vertical plane through the origin, 
and perpendicular to the other two. 

71. 'WoRKiis'G, or KEDUCii^G THE TRAYEESE, is the operation 
of finding the length and direction of a sing-le line, equivalent 
to the zig-zag, that is, starting from, and terminating at, ihe 
same points. Such a line is called the resultant of the traverse. 

The zig-zag line is run along the subterranean openings of 
a mine. For the sake of uniformity, such openings, when ver- 
tical, will be called sliafts, and when not vertical, galleries. 



SEC. v.] MINING SUEVEYING. 261 

Method of traversing with the Compass and Semicircle. 

72. In ruuning a subterranean traverse with, the magnetic 
needle, a form of compass is used, called the Jliner's Compass. 
It consists of a compass-box like that of the Surveyor's Com- 
pass, except that the graduation extends from 0° around, by 
the left, to 36-0°. This box is weighted at the bottom, and 
mounted on a universal joint, like the Mariner's Compass. The 
ring that supports the universal joint is provided Tvith. hooks 
for suspending it from a wire stretched along the gallery. When 
so suspended, the box assumes a horizontal position, the diameter 
through the point of the graduated circle falling immediately 
under the wire ; if the compass be so suspended that the end 
of this diameter points backward, and the 180° end in the 
direction the traverse is being run, the reading at the north 
end of the needle is the angular distance from the north point, 
around by the east to the direction of the course : this angle 
is called the Azimuth of the Course. 

Miner's Semicircle. 

73. The slope of the Course is measured by the Minei^s 
Se7nicircle. This is a graduated semicircle, with hooks, for sus- 
pending it from a stretched wire, and a plumb-line attached 
at the centre of the circle. When suspended, the plane of the 
semicircle is vertical, and its diameter is parallel to the wire; 
the point of the graduation is at the extremity of the radius 
which is perpendicular to the wire, and, as the divisions are 
numbered both ways, the reading of the plumb-line gives the 
slope. As it is impossible to stretch a wire so that it shall 
be perfectly straight, the slope measured at different points will 
not be the same; a fair result will be obtained by measuring 
the- slope at each end of the wire, and taking the average as 
the true slope. 



262 



ELEMENTS OF SUEYEYING. 



[book ni. 



74. To run a traverse, with the compass and semicircle, a 
copper wire is stretched from the place of beginning, say at 
the bottom of the shaft, to some convenient point of the gallery, 
and both ends made fast to iron hooks, driven into the walls 
of the gallery; the compass is suspended from this, at some 
point near its middle, and after it comes to rest, the azimuth 
of the course is read off and recorded; the semicircle is then 
suspended, first, near one end of the wire and then near the 
other, and the average reading is recorded, care being taken 
to note whether the slope is in elevation or dejoression ; the 
length of the ware, from hook to hook, is then measured and 
entered in the field-book. If necessary, measurements are made 
to determine the cross section of the gallery, at any desired 
point of the course, and the results entered in the column of 
remarks. The wire is then detached from the hooks and car- 
ried forward along the gallery, one end being made fast at 
the extremity of the first course, and the other at some con- 
venient point, generally on the opposite side of the gallery; 
the same measurements are made as before and recorded under 
the proper headings, and so on, to the end of the traverse. The 
method of entering the field-notes, is shown in the following 

Field Book. 





Slope. 


Azimuth. 


Length 
in feet. 


Eemakks. 


Course. 


Elevation. 


Depression. 


1 

2 
3 
4 
5 
6 




2° 30' 

3° 15' 
3° 30' 
4° 15' 


203° 

199° 15' 
251° 30' 

300° 00' 
269° 15' 
272° 45' 


307 
402 
240 
367 
409 
200 


Stat. 1, at iron peg, 
centre of shaft. 

At iron peg. 






1° 30' 
2° 00' 







SEC. v.] MINING SURVEYING. 263 

Method of Traversing with the Theodolite. 

75. In traversing with the theodolite, it becomes necessary 
to illuminate the cross hairs of the diaphragm. This is accom- 
plished by a diagonal mirror, placed in front of the object-lens 
of the telescope. The mirror is supported by a stem projecting 
from a ring that surrounds the tube of the telescope, and has 
an opening in the prolongation of the tube, so as not to in- 
tercept the rays of light from the object. A lamp, placed on 
one side of the theodolite, illuminates the remainder of the 
mirror, and, if properly situated, a portion of its light is reflected 
into the tube of the telescope and thrown on the cross hairs. 
Sometimes the theodolite is famished with three tripods exactly 
alike, upon each of which the instrument is mounted in turn, 
the other two serving to support the guiding lamps, which, 
are so constructed that the flame of the lamp shall be as far 
above the top of the tripod as the axis of the vertical limb. 
Sometimes a single tripod is used, in which case the guiding 
lamps are placed on stands similar to the tripods, but with 
sliding pieces carrying the lamps, and fixed in position by 
clamp-screws. By this arrangement, the height of the lamp 
may be made equal to that of the theodolite. The lamps are 
protected by glass shades, of any color that may be desired. 

To run a Traverse with a Theodolite having three Tripods. 

76. Select a place for the first station, say at the foot of 
the shaft, and mark it permanently; set up a tripod over it, 
and place a station lamp on it : select a second station at 
some suitable point, generally at a turn in the gallery, set up 
a tripod over it, and on it put the theodolite : at fhe third 
station, still further along the gallery, set up the third tripod, 
and on it put a station lamp. The theodolite being levelled 
and the horizontal limb clamped, direct the telescope to the 
lamp at the first station, and read both limbs; the reading of 



264: 



ELEMENTS OF SURVEYING. 



[BOOK III. 



the Tertical limb will be the slope of the first course, in eleva- 
tio7i, if tlie telescope point downward — in de^jression, if it 
point upward; then nnclamp the vernier plate, and direct the 
telescope to the lamp at the third station, reading both limbs 
as before ; the reading of the yertical limb will be the slope 
of the second course, in elevation, if the telescope point upward — 
in depressioUy if it point downward ; subtract the first reading 
on the horizontal limb from the second (the latter increased 
by 360° if the of the vernier has passed the of the limb), 
and the difference will be the horizontal angle between the 
first and second courses. 

The distance from the first to the second station is measured 
by chainiDg along the slope, the allignment being made by 
means of lamps, and the points corresponding to the ends of 
chains marked, by chalk-lines on the rock, or in some other 
convenient manner. The theodolite is then transferred to the 
third tripod, its place being taken by a station lamp, and the 
first tripod and lamp are carried along the gallery to mark 
the place of the fourth station; the same observations and 
measurements are made as before, and so on to the end of the 
traverse. The observations are recorded as shown in the fol- 
lowing 

Field Book. 



I 

Sta- 
tion. 


Slope. 


Reading on hor. linib. 


Horizontal 

Angle. 


Dist. 
in feet. 


Kemarks. 


Elevation. 


Depression. 


Back. 


Fore. 


1 

2 




2° 30' 
3° 15' 


107° 20' 


283° 35' 


176° 15' 


307 


Station 1, at iron 
peg, centre of 
shaft. 


3 




3° 30' 


271° 15' 


143° 30' 


232° 15' 


402 




4 




4° 15' 


109° 8' 


337° 38' 


228° 30' 


240 




5 


1^ 80' 




225° 15' 


14° 30' 


149° 15' 


367 




6 


2^00' 




15° 20' 


198° 50' 


183° 30' 


409 




7 










. 


200 


At iron peg. 



When the bearing of the first course is known, the azimuth 
of that, and of the following courses, may bo found, and the 



SEC. v.] 



MINING SURVEYING. 



265 



field-book, thus reduced to the form given in Art. 72. Some- 
times, the first course is assumed as a line of departure, and 
the azimuths of the following courses are calculated with refer- 
ence to it. 



Modes of connecting with Surface Survey. 

77. In order to determine the bearing of the first course, and 
also to be able to trace out the plan of the mine on the ground, 
it is often desirable to connect the underground traverse with 
the surface survey. There are two principal methods of making 
the connection. 




..^^^^^^ 



FIRST METHOD. 

A straight-edge, AB, is mounted on two trestles, and from 
it are suspended two plumb lines, B and F, as far apart as the 
breadth of the shaft will permit. To prevent agitation from 
currents of air, the bobs are permitted to dip into buckets of 
water, at the bottom of the shaft; the theodolite being at the 



2GG 



ELEMENTS OF SURVEYING. 



[book in. 



second station, K, and the telescope turned in the direction of 
the first station, D, the straight-edge is moved by an assistant 
until both are seen in line from K ; their plane then passes 
through the first course; and if the line ^^ be prolonged to 
M and L, the line ML will be directly oyer the first course, and 
consequently its bearing will be that of the first course. By 
measuring the line E, the depth of the shaft may be found. 




SECON-D METHOD. 

Let the theodolite, provided with a diagonal eye-piece, be 
planted over the station JD, at the foot of the shaft, and after 
being levelled, let it be directed on the station K. Then, with- 
out changing the plane of vision, let the theodolite be directed 
to the top of the shaft, and let an assistant plant two flag rods, 
one at ^ and the other at B, both in the plane of vision, and 
let the line AB be prolonged to L and M, as before. Tlie line 
LM will be in the same vertical plane with the first course, DK. 
Hence, as before, we may determine the bearing of the first 
course of the traverse. ^ 



SEC. Y.] 



MINING SURVEYING. 



267 



Reducing the Traverse 

78. We may now find the azimuths of the yarious courses. 
Suppose the bearing of the first course to be S. 23° W. ; then will 
its azimuth be equal to 180^+23°, or, 203°; the azimuths of 
each of the following courses, in order, may be found by the 
following 

EuLE. — Suhtract 180° from the liorizontal angle, ohserviiig 
that the remainder may le either + or — ; add tlie result to the 
preceding azimuth; if the sum is negative, add 360° to it; if 
positive and greater than 360°, subtract 360° from it; the 
result thus found is the azimuth required. 

Thus, in the given example, the horizontal angle between the 
first and second courses- is 176° 15'; this diminished by 180°, 
gives — 3° 45', which added to the preceding azimuth, 203°, gives 
199° 15' for the azimuth of the second course. In like manner, 
we find the azimuth of the third course, 251° 30', of the fourth, 
300°, of the fifth, 269° 15', and of the sixth, 272° 45'. These are 
the same as are given in the example, in Article 72. 

Having found the data, as given in Article 72, we proceed 
to reduce the traverse as shown in the following 

Office Foe:m:. 



Course. 


Slope in ft. 


Bearing. 


Reduced 
lenjith of 
course. 


Latitude. 


Departure. 


Eleva- 
tion. 


Depres- 
sion. 


X. 


s. 


E. 


W. 


1 

2 
3 
4 
5 
6 


10.7 

7. 


13.4 
22.8 
14.7 
27.2 


s. 23° w. 
s. \W w. 
s. 71i° w. 
N. 60° w. 
s. 89r w. 
X. 87i° w. 


306.7 

401.4 

239.6 

366. 

408.9 

199.9 


183.0 
9.6 


282.3 

379.0 

76.0 

5.3 


.... 
.... 


119.8 
132.0 
227.2 
317.0 
408.8 
199.7 




17.7 


78.1 
17.7 






192.6 


742.6 
192.6 


.... 


1404.5 
0.0 


Result- ! 
ant. . . • . 


60.4 


s. 68i' w 


1508.3 


.... 


550.0 


.... 


14045 



268 ELEMENTS OF SUETETING. [BOOK m. 

The form requires but little explanation. From the azi- 
muth, that is, the angle of the course from the north point 
around by the east, the bearing is easily deduced. The length 
of the course on the slope, multiplied by the sine of the slope, 
gives the distance the course rises or falls, in feet, and the length 
multiplied by the cosine of the slope, gives the reduced length 
of the course, that is, the length that would have been found 
had the course been measured on a horizontal line. The bearing 
and reduced course being found, the latitudes and departures of the 
coui'ses are found in the usual manner. In the example given, 
the resultant course descends 60.4 feet, its southing is 550 feet, 
and its westing 140-1.5 ; hence, its bearing and length on the 
horizontal, may easily be found by known methods. 

If the depth of the shaft is known, this, added to the de- 
pression of the resultant, in feet, gives the distance of the last 
station below the horizontal plane through the mouth of the 
shaft. 

Method of Plotting the Traverse on the Surface. 

79. To plot the traverse on the surface of the earth, we 
lay down the direction of the first course, as already shown: 
on this, measure off, in the usual manner, the reduced length 
of the first course, and mark the end of this distance, by a 
peg ; plant the compass over the peg, set it so that the reading 
of the needle is equal to the bearing of the second course, 
and in this direction measure off the reduced value of the 
second course, and so on to the end. Then will the several 
pegs be exactly over the corresponding stations in the mine. _ 

80. Suppose it were required to sink a shaft, so as to strike 
the gallery at station 6, in the example given in Article 76. 
It has been shown how to locate the point exactly over the 
station, (Art. 75). Let a line of levels be run from the mouth 



SEC. Y.] MIKING SURVEYING. 269 

of the first shaft, to this point, and find the difi'erence of level 
corresponding to the two points. This with the depth of the sta- 
tion, in the mine, below the mouth of the shaft, will make known 
the depth of the shaft. This is a problem that frequently oc- 
curs in mining. 

A similar problem often arises in railroad tunnelling. For 
example, if a tunnel is to be driven through a hill, it is often 
desirable to sink shafts, intermediate to the end headings, so 
as to strike the tunnel. Oftentimes, these shafts are used as 
starting-points for portions of the tunnel which are intended 
to meet the parts that are being opened from the headings. 

Method of Plotting the Traverse on Paper. 

81. To plot the traverse, on paper, we first plot the plan 
by the usual method of plotting compass-work, using the bear- 
ings and the reduced lengths of the courses. This gives the 
general direction of the horizontal projection of the traverse 
run: and from the measurements for cross section, the breadths 
of ^ the gallery, on each side, may be plotted, and thence a 
complete plan of the mine may be constructed. We next j^lot 
the profile of. the traverse, using, as in railroad plotting, two 
scales, one for horizontal distances, and the other and larger 
one, for vertical distances. The relation between the two scales 
will depend upon the circumstances of the case. Sometimes, 
both may be equaL The profile represents the undulation of 
the traverse, without reference to its horizontal deviations. Let 
us conceive vertical planes to be passed through all the courses. 
These will intersect each other in vertical lines. Take the one, 
through the first course, as the one on which the profile is to 
be delineated. Then, beginning with the plane through the 
last course, conceive the other planes to be revolved, in order, 
each about its intersection with the preceding one, to coincide 



270 ELEMENTS OP SURVEYING. [BOOK HI. 

with it, and so on till all are brought into coincidence with 
the fixed one. The lines of the traverse will then be situated 
in one plane, and a plot of them, in this position, will be the 
profile required. The distances from the trayerse to the floor 
and roof of the gallery, at difierent points, enable us to com- 
plete the profile. 



A TABLE 



LOGARITHMS OE NUMBERS 



FROM 1 TO 10,000. 



N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


I 


0-000000 


26 


1-414973 


5i 


1.707570 


76 


I -880814 


2 


o-3oio3o 


27 


i-43i364 


52 


I -716003 


77 


1-886491 


3 


0-477I2I 


28 


1-447158 


53 


1-724276 


78 


1-892095 


4 


0- 602060 


29 


1-462398 


54 


1-732394 


79 


1-897627 


5 


0-698970 


30 


1-477121 


55 


1-740363 


80 


1-903090 


6 


o-778i5i 


3i 


I -491362 


56 


1.748188 


81 


1-908485 


I 


0-845098 


32 


i-5o5i5o 


u 


1-755875 


82 


i-9i38i4 


0-903090 


33 


i-5i85i4 


1-763428 


83 


1-919078 


9 


0.954243 


34 


1-53x479 
1-544068 


59 


1-770852 


84 


1-924279 


10 


I • 000000 


35 


60 


1-778151 


85 


1-929419 


II 


1-041393 


36 


i-5563o3 


61 


1.785330 


86 


1-934498 


12 


1-079181 


11 


1-568202 


62 


1-792392 


87 


1-939519 
1-944483 


i3 


I- 1 13943 


1-579784 


63 


imi 


88 


14 


1-146128 


39 


1-591065 


64 


89 


1-949390 


i5 


1-176091 


40 


I -602060 


65 


1-812913 


90 


1-954243 


i6 


i-ao4i2o 


41 


1-612784 


66 


1.819544 


91 


1-959041 


17 


1-230440 
1-255273 


42 


1-623249 
1-633468 


67 


1-826075 


92 


1.963788 


i8 


43 


68 


1-832509 


93 


1.968483 


^9 


1-278754 


44 


1-643453 


69 


1-838849 
1-845098 


94 


1.973128 


20 


I -301030 


45 


1-653213 


70 


95 


1.977724 


21 


I-3222I9 


46 


1-662758 


71 


I-85I258 


96 


1.982271 


22 


1-342423 


47 


1-672098 
1-681241 


72 


1-857333 


97 


1-986772 


23 


I. 361728 


48 


73 


1-863323 


98 


1.991226 


24 


I-3802II 


49 


I -690196 


74 


1-869232 
1-875061 


99 


1.995635 


25 


1-397940 


5o 


1-698970 


75 


100 


2-000000 



Remark. In the following table, in the nine right hand 
columns of each page, where the first or leading figures 
change from 9's to O's, points or dots are introduced in 
stead of the O's, to catch the eye, and to indicate that from 
thence the two figures of the Logarithm to be taken from 
the second column, stand in the next line below 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 





I 


2 


3 


'^ 


' 


6 


7 


8 


9 1 D. 


100 


000000 


0434 


0868 


i3oi 


1734 


2166 


2598 


3029 


3461 


3891 ; 43a 


101 


4321 


4751 


5i8i 


5609 


6o38 


6466 


6894 


732T 


7748 


8174 


428 


102 


8600 


9026 
3259 


9431 


9876 


•3oo 


•724 


1147 


1570 


1993 


24i5 


424 


io3 


012837 


368o 


4100 


4521 


4940 


536o 


5779 


6197 


6616 


419 


104 


7033 


745 1 


7868 


8284 


8700 


0116 

3252 


til 


9947 


•36 1 


•775 


416 


io5 


021189 


i6o3 


2016 


2428 


2841 


4075 


4486 


4896 


412 


io6 


53o6 


5715 


6125 


6533 


6942 


7350 


11^1 


8164 


8571 


8978 


408 


107 


9384 
033424 


0789 
3826 


•195 


•600 


1004 


1408 


1812 


2216 


2619 


302I 


404 


108 


4227 


4628 


5029 


543o 


5830 


623o 


6629 


7028 


400 


109 


7426 


7825 


8223 


8620 


9017 


9414 


981 1 


•207 


•602 


•998 


396 


no 


041393 


1787 


2182 


2576 


lU 


3362 


3755 


4148 


4540 


4932 


393 

389 


III 


5323 


57.4 


6io5 


6495 


7275 


7664 


8o53 


8442 


883o 


112 


9218 
053078 


9606 
3463 


9993 


•38o 


•qbb 


ii53 


1 538 


1924 


23o9 


2694 


386 


ii3 


3846 


423o 


46i3 


4996 


5378 


5760 


6142 


6524 


382 


114 


6905 


7286 


7666 


8046 


8426 


88o5 


9i85 


9563 
3333 


9942 


•320 


379 


ii5 


060698 
4458 


1075 


1452 


1829 


2206 


2582 


2958 


3709 


4o83 


376 


116 


4832 


5206 


5580 


5953 


6326 


6699 


7071 


7443 


78.5 


372 


\\l 


8186 


8557 


8928 


9298 


f^l 


••38 


•407 


•776 


1.45 


i5i4 


369 


071882 


225o 


2617 


2985 


3718 


4o85 


445 1 


4816 


5i82 


366 


L19 


5547 


5912 


6276 


6640 


7004 


7368 


7731 


8094 


8457 


8819 


363 


I/O 


079181 


9543 


9904 


•266 


•626 


•987 
4576 


1347 


1707 


2067 


2426 


36o 


121 


082785 


3i44 


35o3 


386i 


4219 


4934 


5291 


5647 
9198 


6004 


357 


122 


636o 


6716 


7071 


7426 


7781 


8i36 


8490 


8845 


f^\ 


355 


123 


9905 
093422 


•258 


•611 


•963 


i3i5 


1667 


2018 


2370 


2721 


35i 


124 


3772 


4t22 


4471 


4820 


5169 


55i8 


5866 


62i5 


bbb-} 


349 


125 


6910 


7257 


7604 


7951 


8298 


8644 


8990 


9335 


9681 


••26 


346 


126 


100371 


0715 


1059 


i4o3 


1747 


2091 


2434 


2777 


3.19 


3462 


343 


\ll 


38o4 


4146 


4487 


4828 


5169 


55io 


585 1 


6191 


653 1 


6871. 


340 


7210 


7549 


7888 


8227 


8565 


8903 


9241 


9579 


9916 


•253^ 


338 


129 


1 10590 


0926 


1263 


1599 


1934 


2270 


2605 


2940 


3275 


3609* 


335 


i3o 


II 3943 


4277 


461 1 


4944 


5278 


56ii 


5943 


6276 


6608 


6940 


333 


i3i 


7271 


7603 


7934 


8265 


8595 


8926 


9256 


9586 


99'5 


•245 


33o 


i3i 


1205-^4 


0903 


I23l 


i56o 


1888 


2216 


2544 


2871 


3198 


3525 


328 


i33 


3852 


4178 


45o4 


483o 


5i56 


5481 


58o6 


6i3i 


6456 


6781 


325 


I34 


7105 


7429 


7753 


8076 


8399 


8722 


9045 


9368 


9690 


••12 


323 


i35 


i3o334 


0655 


0977 


1298 


1619 


1939 
5i33 


2260 


258o 


2900 


3219 


321 


i36 


3539 


3858 


4177 


4496 


4814 


545 1 


5769 


6086 


6403 


3i8 


III 


6721 


7037 


7354 


7671 


7987 


83o3 


8618 


8934 


9249 


9564 


3i5 


9879 
i43oiD 


•194 


•5o8 


•822 


ii36 


i45o 


1763 


2076 


2389 


2702 


3i4 


139 


3327 


3639 


3951 


4263 


4574 


4885 


5196 


5507 


58i8 


3ii 


140 


146128 


6438 


6748 


7o58 


7367 


7676 


7985 


8294 


86o3 


891 1 


309 


141 


1 5228? 


9527 


9835 


•142 


•449 


•756 


io63 


1370 


1676 


19S2 


307 


142 


2594 


2900 


32o5 


35,0 


38 1 5 


4120 


4424 


4728 


5o32 


3o5 


143 


5336 


5640 


5943 


6246 


6549 


6852 


7154 


7457 


7739 


8061 


3o3 


144 


8362 


8664 


8q65 


9266 


9567 


9868 


•168 


•469 


•769 


1068 


3oi 


145 


i6i368 


1667 


1967 


2266 


2564 


2863 


3i6i 


3460 


3758 


4o55 


299 


146 


4353 


465o 


4947 


5244 


5541 


5838 


6i34 


6430 


6726 


7022 


297 


147 


7317 


7613 


lit 


82o3 


8497 


8792 


9086 


9380 


9674 


9968 


295 


148 


170262 


o555 


1141 


1434 


1726 


2019 


23ll 


26o3 


2A95 


293 


149 


3i86 


3478 


3769 


4060 


435i 


4641 


4932 


5222 


55x2 


5802 


291 


i5o 


176091 


638i 


6670 


6959 
9S39 


7248 


7536 


7825 


8ii3 


8401 


8689 


289 


i5i 


8977 
181844 


9264 


9552 


•126 


•4i3 


•699 


•985 


1272 


i558 


287 


l52 


2129 


24i5 


2700 


2985 
5825 


3270 


3555 


3839 


4123 


4407 


285 


1 53 


4691 


4970 


5259 


5542 


6108 


6391 


6674 


6956 


7239 


283. 


1 54 


7521 


7803 


8084 


8366 


8647 


8928 


9209 


9490 


9771 


••5i 


281 


i55 


190332 


0612 


0892 
368i 


1171 


I45i 


1730 


2010 


2289 


2567 


2846 


'il 


1 56 


3125 


3403 


3959 


4237 


45i4 


4792 


5069 


5346 


5623 


i57 


5899 


6176 


6453 


6729 


7005 


7281 


7536 


7832 


^'?'' 


83.S2 


276 


i58 


8607 


8932 
1670 


9206 


9481 


9755 


••29 


•3o3 


•577 


•85o 


1124 


274 


159 
N. 


201397 


1943 


2216 


2488 


2761 


3o33 


33o5 


3577 


3848 
9 


272 





I 


2 


3 


^ 


5 


6 


7 


8 



TABLE OF LOGARITHMS FRO:m: 1 TO 10,000. 



N. 


j I 


2 


1 3 


4 


5 1 6 


j 7 1 8 


9 


D. 

271 


l6o |2o4i2o 4391 


4663 


4934 


5204 


5475 ' 5746 


6016 6286 


6556 


161 


6826 7096 


7365 


7634 


7904 


8173 8441 


8710 


8970 


9247 


269 


162 


95 1 5 9783 


••5 1 


•3.9 


•586 


•853 1 121 


i388 


i654 


1921 


267 


163 


212188 2454 


2720 


2986 


3252 


35 1 8 3783 j 4049 


43i4 


4579 


166 


164 


4844 5 1 09 


5373 


5638 


5902 


6166 643o 


6694 


6957 i 7221 


264! 


l65 


7484 7747 


8010 


8273 


8536 


8798 


9060 


9823 


9585 ! 9846 262 


166 


i >oio8 


0370 


o63i 


0892 


ii53 


1414 


1675 


1986 


2196 2456 i 261 


167 


2716 


2976 


3236 


3496 


3755 


401 5 1 4274 


4533 


4792 5o5h 25a 


168 


5309 


5568 


5826 


6084 


6342 


6600 


6858 


7115 


7872 7680 


i 25a 


169 


7887 


8144 


8400 


8657 


8913 


9170 


9426 


9682 


9938 


•193 


256 


170 


330449 


0704 


0960 


12l5 


1470 


1724 


1979 


2234 


2488 


2742 


254 


171 


2996 


325o 


35o4 


3757 


40 1 1 


4264 


4517 


4770 


5o23 


5276 


253 


172 


5528 


5781 


6o33 


6285 


6537 


67S9 


7041 


7292 


7544 


7795 


252 


173 


8046 


8297 


8548 


8799 


9049 


9299 


9350 


9800 


••30 


•3oo 


' 25o 


174 


240549 


0799 


1048 


1297 


1 546 


1793 


2044 


2293 


2541 


2790 


249 


175 


3o3S 


3286 


3534 


3782 


4o3o 


4277 


4525 


4772 


5019 


5266 


248 


176- 


55i3 


5759 


6006 


6252 


6499 


6745 


6991 


7237 


7482 


7728 


246 


\]l 


7973 


8219 


8464 


8709 


8934 
1395 


9198 


9443 


9687 


ttl 


•176 


245 


25o420 


0664 


0Q08 


ii5i 


1633 


1881 


2125 


2610 


243 


179 


2853 


3096 


3338 


3580 


3822 


4064 


43o6 


4548 


4790 


5o3i 


242 


180 


255273 


55i4 


5755 


5996 


6237 


6477 


6718 


6958 


7198 


7439 


241 


181 


7679 


7918 
o3io 


8i58 


83qS 
0787 


8637 


8877 


9116 


9355 


9594 


9833 


23o 
23S 


182 


260071 


0548 


1025 


1263 


i5oi 


1789 


4346 


2214 


i83 


245 1 


2688 


2925 


3i62 


3399 


3636 


3873 


4109 


4582 


287 


184 


4818 


5o54 


5290 


5525 


5761 


5996 


6232 


6467 


6702 


6987 


235 


1 85 


7172 


7406 


7641 


7875 


8IIO 


8344 


8578 


8812 


9046 


9279 


284. i 


186 


95i3 


9746 


9980 


•2l3 


•446 


•679 


•912 


II44 


1877 


1609 


233 j 


187 
188 


271842 


2074 
4389 


23o6 


2533 


2770 


3ooi 


3233 


3464 


3696 


3927 


282! 


4i58 


4620 


4S5o 


5o8i 


53 II 


5542 


5772 


6002 


6232 


280 


189 


6462 


6692 


6921 


7i5i 


7380 


7609 


7838 


8067 


8296 


8525 


229. 


190 


27^^754 


8982 


9211 


',f.t 


9667 


9895 


•123 


•35i 


•578 


•806 


228 


191 281033 


1261 


1488 


1942 


2169 


2396 


2622 


2849 


8075 


227 


192 


33oi 


3527 


3753 


3979 


42o5 


443 1 


4656 


4882 


5107 


5332 


226. 


193 


5557 


5782 


6007 


6232 


6456 


6681 


6905 


7180 


7354 


7578 


225 


194 


7S02 


8026 


8249 


8473 


8696 


8920 


9143 


9866 


9589 
i8i3 


9S12 


223 


195 


290035 


0257 


04B0 


0702 


0925 


1 147 


1869 


1591 


2084 


222 


196 


2256 


2478 


2699 


2920 


3i4i 


3363 


3584 


38o4 


4025 


4246 


221 


197 


4466 


4687 


4907 


5i27 


5347 


5567 


5787 


6007 
8198 


6226 


6446 


220 


198 


6665 


6S84 


7104 


7323 


7542 


7761 


7979 


8416 


8635 


2ia 

218 


199 8853 


9071 


9289 


9507 


9725 


9943 


•161 


•378 


•595 •8i3 


2CO 3oio3o 


1247 


1464 


1681 


1898 


2114 


233 1 


2547 


2764 


2980 


217 


201 3 1 96 


3412 


3628 


3844 


4039 


4275 


4491 


4706 


4921 


5i36 


21^ 


202 53 5 I 


5566 


5781 


5996 


6211 


6425 


6639 


6854 


7068 


7282 


2l5 


203 7496 

204 9630 


7710 


7924 


8^37 


835i 


8564 


8778 


8991 


9204 


9417 


2l3 


9843 


••56 


•268 


•481 


•693 


•906 


1118 


i33o 


i542 


212! 


2o5 3 1 1754 


1966 


2177 


2389 


2600 


2812 


3o23 


3234 


3445 


3656 


2ll| 


206 


3867 


4078 


4289 


4499 


4710 


4920 


5i3o 


5340 


5551 


5760 


2I0J 


III 


5970 


6180 


6390 


6599 


6809 


7018 


7227 


7436 


7646 


7854 


12 


8o63 


8272 


8481 


8689 


8898 


9106 


9814 


9522 


9730 


9988 


209 :320I46 


o354 


o562 


0769 


0977 


1 184 


1891 


1598 


i8o5 


2012 


207 


210 


322219 


2426 


2633 


2839 


3046 


3252 


3458 


3665 


3871 


4077 


sd6 


2H 


4282 


4488 


4694 


4899 


5io5 


53io 


55i6 


5721 


5926 


6i3i 


:o5 


ai2 


6336 


6541 


6745 


6950 


7x55 


7359 


7563 


7767 


7972 


8176 


2041 


3l3 


838o 


8583 


8787 


8991 


9194 


9398 


9601 


9805 


•••8 


•211 


2o3J 


214 1330414 


b6i7 


0819 


1022 


1223 


1427 


i63o 


i832 


2o34 


2236 


202] 


2l5 


2438 


2640 


2842 


3o44 


3246 


3447 


3649 


385o 


4o5i 


4253 


202 


216 


4454 


4655 


4856 


5o57 


5257 


5458 


5658 


5859 


6059 


6260 


201 


l\l 


6460 6660 


6860 


7060 


7260 


7459 


7659 


7858 


8o58 ! 8237 1 


200 j 


8456 8656 


8855 


9054 


9253 


945 1 


9650 


9849 


••47 ■: •246 


I90J 


219 340444 0642 


0841 


1039 


1237 


1435 


i632 


i83o 


2028 ; 2225 1 I93-I 


N. 1 I. 


2 


' 


4 


5 


6 


7 


8 1 9 


^ 



15 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



|n. 


1 1 


2 


3 


4 


5 


6 


7 


8 


9 


dTI 


220 


342423 2t)20 


2817 


3oi4 


3212 


3409 


36o6 


38o2 


3999 


4196 


\U 


221 


4392 4389 


4785 


4981 


5178 


5374 


5570 


5766 


5962 


6i?7 


! 222 


63d3 6549 


6744 


^ 


7135 


7330 


7525 


7720 


79i5 


8110 


195 


! 223 


83o5 85oo 


8694 


9083 


9278 


9472 


9666 


9860 


••54 


1^4 


1 224 


350248 0442 


0636 


0829 


1023 


1216 


1410 


i6o3 


1796 


1989 


193 


t 225 


2i83 2375 


2568 


2761 


2954 


3i47 


3339 


3532 


3724 


3916 


193 


1 226 


4108 43oi 


4493 


4685 


4876 


5o68 


5260 


5452 


5643 


5834 


19a 


227 


6026 6217 


6408 


6599 


6790 


6981 


7172 


7363 


7554 


7744 


191 


228 


7935 8i25 


83i6 


85o6 


8696 


8886 


9076 


9266 


9456 


9646 


190 


229 


9835 ••25 


•210 


•404 


•593 


•7S3 


•972 


1161 


l330 


1539 


189 


23o 


''^ lU 


2io5 


2294 


2482 


2671 


2859 


3048 


3236 


3424 


188 


23l 


3988 


4176 


4363 


455i 


4739 


4926 


5ii3 


53oi 


188 


232 


5488; 5675 


5862 


6049 


6236 


6423 


6610 


6796 


6983 


7169 


187 


233 


7356! 7542 


7729 


79ID 


8101 


8287 


8473 


8639 
•5i3 


8845 


9o3o 


186 


234 


9216; 9401 


9087 


9772 


995^ 


•328 


•698 


•883 


i85 


235 


371068 1253 


1437 


1622 


J 806 


I'Sl 


2175 


236o 


2544 


2728 


184 


236 ) 


2912 3096 
4748 4932 


3280 


3464 


3647 


401 5 


4198 


4382 


4565 


184 


237 


5ii5 


5298 


5481 


5664 


5846 


6029 


6212 


6394 


i83 


238 


6577 


6759 


6942 


7124 


7306 


7488 


7670 


7852 


8o34 


8216 


182 


239 


8398 


858o 


8761 


8943 


9124 


9306 


9487 


9668 


9849 


••3o 


181 


240 


3802II 


0392 


0573 


0754 


0934 


iii5 


1296 


1476 


i656 


1837 


181 


241 


2017 


2197 


2377 


2557 


2737 


2917 


3097 


3277 


3456 


3636 


180 


242 


38i5| 3995 


4174 


4353 


4533 


4712 


4891 


5070 


5249 


5428 


179 


243 


56o6 5780 


5964 


6142 


6321 


6499 


6677 


6856 


7034 


7212 
8989 


178 


244 


7390 7568 


7746 


7923 


8101 


8279 


8456 


8634 


88n 


178 


245 


9166 9343 


9^^° 


9698 


9875 


••5 1 


•228 


•4o5 


•582 


•759 


177 


246 


390935 


1112 


1288 


1464 


1641 


1817 


1993 


2169 


2345 


2321 


176 


247 


2697 

4432 


2873 


3048 


3224 


3400 


3575 


37DI 


3926 


4101 


4277 


17^ 


248 


4627 


4802 


4977 


5i52 


5326 


5doi 


5676 


5850 


6025 


175 


249 


6199 


6374 


6548 


6722 


6896 


7071 


7245 


7419 


7592 


7766 


174 


25o 


397940 


8114 


8287 


8461 


8634 


8808 


8981 


9154 


9328 


95oi 


173 


25l 


9674 


9847 


••20 


•192 


•365 


•538 


•711 


•883 


io56 


1228 


173 


252 


401401 


i573 


1745 


1917 


2089 


2261 


2433 


26o5 


2777 


2949 


172 


253 


3l2I 


3292 


3464 


3635 


3807 


3978 


4149 


4320 


4492 


4663 


171 


254 


4834 


5oo5 


5176 


5346 


5517 


5688 


5858 


6029 


6199 


6370 


171 


255 


6540 


6710 


6881 


7o5i 
8749 


7221 


7391 


756i 


7731 


7901 


8070 


170 


256 


8240 


8410 


8579 


8918 


9087 


92D7 


9426 


Ul 


9764 


169 


257 


9933 


•102 


•271 


•440 


•609 
2293 


•777 


•946 


1114 


I45i 


\tt 


258 


411620 


1788 


1956 


2124 


2461 


2629 


2796 


2964 


3i32 


259 


33oo 


3467 


3635 


38o3 


3970 


4i37 


43oD 


4472 


4639 


4806 


167 


260 


414973 


5i4o 


5307 


5474 


5641 


58o8 


^n^ 


6141 


63o8 


6474 


167 


261 


6641 


6807 


6973 


lf,t 


7306 


7472 


7638 


7804 


7970 


8i35 


166 


262 


83oi 


8467 


8b33 


8964 


9129 


9295 


9460 


9625 


9791 


i65 


263 


9956 


•121 


•286 


•45i 


•616 


•781 


•943 
2390 


IIIO 


1275 


1439 


i65 


264 


421604 


1788 


1933 


2007 
3737 


2261 


2426 


2754 


2918 


3082 


164 


265 


3246 


3410 


3574 


3901 


4o65 


4228 


4392 


4555 


4718 


164 


266 


4882 


5045 


5208 


5371 


5d34 


5697 


586o 


6023 


6186 


6349 


i63 


267 


65ii 


6674 


6836 


6999 


7161 
8783 


7324 
8944 


7486 


7648 


781 1 


7973 


162 


268 


8i35 


8297 


8459 


8621 


9106 


ni^ 


9429 


9591 


162 


259 


9752 


9914 


••7! 


•236 


•398 


•559 


•720 


•881 


1042 


I203 


161 


270 


43 1 364 


1 525 


i685 


1846 


2007 


2167 


2328 


2488 


2649 


2809 


161 


271 


6i63 


3i3o 


3290 


3450 


36io 


3770 


3930 


56^5 


4249 


4409 


160 


272 


4729 


4888 


5048 


5207 


5367 


5526 


5844 


6004 


1 59 


273 


6322 


6481 


6640 


6708 


6957 


7116 


7275 


7433 


7592 


is? 


274 


7751 


7909 


8067 
9648 


8226 


8384 


8542 


8701 


8859 


9017 


9173 


275 


9333 


9491 


9806 


tsi 


•122 


•279 


•437 


•594 


•752 


1 58 


276 


440909 


1066 


1224 


i38i 


1695 


i852 


2009 


2166 


2323 


1 57 


27T 
27$ 


2480 


2637 


2793 
4357 


2950 


3io6 


3263 


3419 


3576 


3732 


3889 


1 57 


4045 


4201 


4313 


4669 


4825 


4981 


5i37 


5293 


5449 

7003 


1 56 


279 


5604 


5760 


5915 


6071 


6226 


6382 


6537 


6692 


6848 


i55 


N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


D. 



A TABLE OF LOGARITHMS FROM 1 TO ICjOOO. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


3S0 


447158 


73i3 


7468 


7623 


7778 


7933 


8088 


8242 


8397 


8552 


1 55 


281 


8706 


8861 


9oi5 


9170 


9324 


9478 


9633 


9787 


9941 


••95 
1 633 


1 54 


282 


450249 


o4o3 


0557 


071 1 


0865 


1018 


1172 


i326 


1479 


i54 


283 


1786 


1940 


2093 


2247 


2400 


2553 


2706 


2809 


30I2 


3i65 


1 53 


284 


33i8 


3471 


3624 


3777 


3930 


4082 


4235 


4387 


4540 • 4692 


1 53 


285 


4845 


4997 


5i5o 


53o2 


5454 


56o6 


5758 


5910 


6062 1 6ji4 


l52 


286 


6366 


65i8 


6670 


6821 


6973 


7125 
8638 


7276 
8789 


7428 


7579 


7731 


X52 


287 


7882 


8o33 


8184 


8330 


8487 


8940 


9091 


9-42 


x5i 


288 


9392 


9543 


9694 


9845 


9995 


•146 


•296 


•447 


•597 


•748 


x5x 


289 


460898 


I048 


1198 


i348 


1499 


1649 


1799 


1948 


2098 


2248 


x5o 


290 


462398 


2548 


2697 


2847 


2997 


3146 


3296 

4788 


3445 


3594 


3744 


i5o 


291 


3893 


4042 


4191 
568o 


4340 


4490 


4639 


4936 


5o85 


5234 


149 


292 


5383 


5532 


5829 


5977 


6126 


6274 


6423 


6571 


6719 


149 


293 


6868 


7016 


7164 


7312 


7460 


7608 


7756 


7904 


8o52 


8200 


148 


294 


8347 


8495 


8643 


8790 


8938 


9085 


9233 


9380 


9527 


9675 


X48 


295 


9822 


9969 


•116 


•263 


•410 


•557 


•704 


•85i 


•998 


1 145 


J 47 


296 


471295 
2756 


1438 


i585 


1732 


1878 


2025 


2171 


23i8 


2464 


2610 


X46 


297 


2903 
4362 


3o49 


3195 
4653 


3341 


3487 


3633 


3779 
5235 


3925 


4071 


146 


298 


4216 


45o8 


tin 


4944 


5090 


538i 


5526 


146 


299 


5671 


58i6 


5962 


6107 


6397 


6542 


6687 


6832 


6976 


145 


3oo 


477121 


7266 
8711 


741 1 


7555 


7700 


7844 


7989 


8i33 


8278 


8422 


145 


3oi 


8566 


8855 


8999 


9143 


9287 


9431 


9575 


9719 


9863 


144 


302 


480007 


oi5i 


0294 


0438 


0582 


0725 


0869 


1012 


ii56 


1299 


144 


3o3 


1443 


1 586 


1729 


1872 


2016 


2159 


23o2 


2445 


2588 


273i 


143 


3o4 


2874 


3oi6 


3i59 
4585 


33o2 


3445 


3587 


3730 


3872 


4oi5 


4157 


X43 


3o5 


43oo 


4442 


4727 


4869 


5oii 


5i53 


5295 


5437 


5579 


142 


3o6 


5721 


5863 


6oo5 


6147 


6289 


643 


6572 


6714 


6855 


6997 


142 


3o7 


7i38 
855i 


7280 


7421 


7563 


7704 


7845 


7986 
9396 


8127 


8269 


8410 


141 


3oa 


8692 


8833 


8974 


9114 


9255 


9537 


9677 


9818 


141 


3o9 


9958 


••99 


•239 


•38o 


•520 


•661 


•801 


•941 


1081 


1222 


140 


3io 


491362 


l502 


1642 


1782 


1922 


2062 


2201 


2341 


2481 


2621 


140 


3ii 


2760 


2900 


3 040 


3179 


3319 


3458 


3597 
4989 


3737 


3876 


401 5 


x39 


3l2 


4i55 


4294 


4433 


4572 


47II 


485o 


5128 


5267 


5406 


139 


3i3 


5544 


5683 


5822 


5960 


6099 

7483 


6238 


6376 


65i5 


6653 


6791 


i3q 

i3g 


3i4 


6930 
83ii 


7068 


7206 


7344 


7621 


7759 


7897 


8o35 


8173 


3i5 


8448 


8586 


8724 


8862 


8999 


9137 


9275 


9412 


9550 


i38 


3i6 


9687 


9824 


9962 


••99 


•236 


•374 


•5ii 


•648 


•785 


•922 


137 


3i7 
3i8 


5oio59 


1 196 


1333 


1470 


1607 


1744 


1880 


2017 


2X54 


2291 
3655 


137 


2427 


2564 


27CO 


2837 


2973 
4335 


3109 


3246 


3382 


35i8 


i36 


3i9 


3791 


3927 


4o63 


4199 


4471 


4607 


4743 


4878 


5oi4 


i36 


3 20 


5o5i5o 


5286 


5421 


5557 


5693 


5828 


5o64 
73i6 


6099 


6234 


6370 


i36 


321 


65o5 


6640 


6776 


691 1 


7046 


7181 


745f 


7586 


7721 


i35 


322 


7856 


1% 


8126 


8260 


8395 


8530 


8664 


8799 


8934 


9068 


i35 


323 


9203 


9471 


9606 


9740 


9874 


•••9 


•143 


•277 


•4x1 


x34 


324 


5io545 


0679 


o8i3 


0947 


1081 


12l5 


1 349 


1482 


1616 


1750 


x34 


325 


1 883 


2017 


2l5l 


2284 


2418 i 


255i 


2684 


2818 


2951 


3o84 


:33 


326 


3218 


335 1 


3484 


36i7 


3750 ; 3883 1 


4016 


4i4q 


4282 


4414 


x33 


327 


4548 


4681 


48i3 


4946 


5079 i 


52II 


5344 5476 


5609 


5741 


x33 


328 


5874 


6006 


6139 


6271 


64o3 


6535 


6668 6800 


6932 


7064 
8382 


I32 


329 


7196 


7328 


7460 


7592 


7724 


7855 


7987 81 19 


825i 


l32 


33o 


Ii85i4 


864i 


8777 


8909 


9040 


9171 


93o3 


9434 


9566 


9697 


i3i 


33 1 


9828 


9959 


••90 •22 X 


•353 


•484 


•6i5 


•745 


•876 


X007 


i3x 


332 


52u38 


257? 


1400 i53o 


i66i 


1792 


1922 


2053 


2i83 


23x4 


x3i 


333 


2444 


2705 i 2835 


2966 


3096 


3226 


3356 


3486 


36x6 


x3o 


334 


3746 


3876 


4006 41 36 


4266 


4396 


4526 


4656 


4785 


491 5 


i3o 


335 


5o45 


5174 
6469 


53o4 5434 


5563 


6985 


5822 


595 1 


6081 1 6210 1 


X29 


336 


6339 


6598 6727 


6856 


7II4 


7243 


7372 


7501 


X29 


337 


7630 


7759 


7888 


8016 


8145 


8274 


8402 


853 r 


8660 


8788 


lit 


338 


8917 


9045 


9174 


9302 


943o 


9559 


9687 


9815 


9943 


••72 


339 

N. 


530200 


o328 


0456 


o584 


0712 


0840 


0968 


1096 


1223 


i35x 


128 





» 


2 


3 


4 


' 1 


6 


7 


~ 


' 


D. 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


j I 


2 


3 


4 


5 


6 


7 


8 


9 

2627 


D. 

laS 


"3^ 


531479 1607 


1734 


1862 


1990 


2117 


2245 


2372 


25oo 


341 


2754 28a2 


3009 


3i36 


3264 


3391 


35i8 


3645 


3772 


3899 


127 


342 


4026 4i53 


4280 


4407 


4534 


4661 


4787 


4914 


5o4i 


5.67 


127 


343 


5294 5421 


5547 


5b74 


58oo 


5927 


6o53 


6180 


63o6 


6432 


126 


344 


6558 66>:)5 


68u 


6937 


7063 


7189 


73i5 


7441 


7567 


7693 


126 


34:3 


7819 7Q45 


8071 


8.97 


8322 


8448 


8574 


8699 


8825 


8951 


126 


346 


9076 9202 


9327 


9402 


9578 


97o3 


9829 


9954 


••79 


•204 


123 


347 


f^oJ29 0455 


o58o 


0705 


o83o 


0955 


1080 


I205 


i33o 


1454 


123 


34rf 


1 579 1704 


1829 


1953 


2078 


2203 


2327 


2452 


2576 


2701 


125 


349 


"825 2950 


^074 


3199 


3323 


3447 


3571 


3696 


3820 


1944 


124 


350 


i 44068 4192 


43i6 


4440 


4564 


4688 


4812 


4936 


5o6o 


5i83 


124 


331 


5307 543 1 


5555 


5678 


5d02 


5925 


6049 


6.72 


6296 


6419 


124 


352 


6543 6666 


6789 


6913 


7o36 


7159 


7202 


74o5 


7529 
8758 


76J2 


123 


353 


7775 7«9^ 


8021 


8144 


8267 


83 89 


85i2 


8635 


8881 


123 


354 


90')3 9126 


9249 


9371 


9494 


9616 


9739 


9861 


9984 


•106 


123 


350 


550228 o35i 


0473 


0595 


0717 


0840 


0962 


1084 


1206 


i328 


J22 


350 


1450 1572 


1694 


1816 


1938 


2060 


2181 


23o3 


2425 


2547 


122 


357 


2668 2790 


2911 


3o33 


3.55 


3276 


3398 


3519 


3640 


3762 


121 


35rf 


3883 4004 


4126 


4247 


4368 


44H9 


4610 


4731 


4852 


4973 


121 


359 


5094 521 5 


5336 


5457 


5578 


5699 


5820 


5940 


6061 


6182 


121 


360 


5563o3' 6423 


6544 


6664 


6785 


6905 


7026 


7146 


7267 


7387 


120 


361 


7507 7627 


7748 


7^68 


79^8 


8108 


8228 


8349 


8469 


8589 


"120 


362 


8709 8S?9 


8948 


9068 


9.88 


9308 


9428 


9548 


9667 


9787 


120 


363 


9907 •*26 


•146 


•205 


•385 


•5o4 


•624 


•743 


•863 


•982 


119 


364 


56 1 1 1 1221 


1 340 


1459 


1578 


1698 


1817 


1936 


2o55 


2174 


119 


36J 


2293 2412 


253i 


26JO 


2769 


2887 


3oo6 


3i25 


3244 


3362 


119 


366 


3481 3600 


3718 


3.^37 


3930 


4074 


4192 


43ii 


4429 


45^8 


119 


367 


4666 1 4784 


4903 


502I 


5i39 


5257 


D376 


5494 


56i2 


5730 


(18 


36tf 


5848; 5966 


6084 


6202 


6320 


6437 


6555 


6673 


6791 


6909 


118 


369 


70261 7144 


7262 


7379 


7497 


7614 


7732 


7849 


7967 


8084 


118 


370 


5682021 83i9 


8436 


8554 


8671 


8788 


8905 


9023 


91 40 


9207 


•17 


371 


9374' 9491 


9608 


9725 


9842 


9959 


-76 


•193 


•309 


•426 


»i7 


372 


570543 1 0060 


0776 


0893 


1010 


1126 


1243 


1359 


1476 


1592 


117 


373 


1709: I«25 


1942 


2008 


2174 


2291 


2407 
3568 


2523 


2639 


2755 


116 


374 


20721 2088 


3io4 


3220 


3336 


3452 


3684 


3800 


3915 


116 


370 


4o3i 


4147 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


116 


376 


5i88 


53o3 


5419 


5534 


5o5o 


5765 


588o 


5996 


6111 


6226 


ii5 


377 


6341 


6457 


6572 


6687 


6802 


6917 


7o32 


7147 


7262 


7377 


ii5 


37rf 


7492 7607 


7722 


7836 


7951 


8ob6 


8181 


8295 


8410 


8525 


ii5 


379 


8639 8754 


8868 


8983 


9097 


9212 


9326 


9441 


9555 


9669 


114 


380 


579784 9S98 


••12 


•126 


•241 


•355 


Zl 


•583 


•697 


•811 


114 


381 


580925! 1039 


II 53 


1267 


1 38 1 


2631 


1722 


1 836 


1950 


114 


382 


20631 2177 


2291 


2404 


25i8 


2745 


2858 


2972 


3o85 


114 


383 


3iQ9; 33i2 


3^26 


3j39 


3652 


3765 


3879 


3992 


4105 


42 i 8 


ii3 


384 


433 1 4444 


4557 


4670 


4783 


4896 


D009 


5,22 


5235 


53^j 


ii3 


385 


5461 


5574 


5686 


5799 


5912 


6024 


6,37 


6250 


6362 


6475 


ii3 


386 


6587 


6700 


6812 


6925 


7037 


7'49 


7262 
8384 


6496 


7486 


7599 


112 


387 


7711 


7823 


7935 


8047 


8160 


8272 


8608 


8720 


112 


388 


8832 


3o44 


9o56 


9167 


9279 


9391 


95o3 


96i5 


9726 


983S 


ri2 


389 


9950 ••61 


•n3 


•284 


•396 


•5o7 


•619 


•730 


•842 


•953 


112 


39c 


591065 1176 


1287 


1399 


i5io 


1621 


2843 


1843 


t955 


2066 


Hi 


391 


2177 2288 


2399 


25 10 


2621 


2732 


2954 


3064 


3175 


III 


39s 


3286 3397 


35o8 


36i8 


3729 


3840 


3950 


406 1 


4171 


4282 


111 


393 


4393 45o3 


4614 


4724 


4834 


4945 


5o55 


5i65 


5276 


5386 


110 


394 


54961 56o6 


5717 


5827 


5937 


6047 


6i57 


6267 


6377 


^^uZ 


no 


395 


65971 6707 


6817 


^9:7 


7037 


7146 


7256 


7366 


7476 


7D86 


IlOi 


396 


76951 7805 


79'4 


So24 


8i34 


8243 


8353 


8462 


8572 


8681 


no 


397 


8791 


8900 


9009 


9119 


9228 


9337 


9446 


9556 


9665 


m^ 


109 


398 


9883 


9992 


•lOI 


•2n 


•3i9 


•428 


•537 


•646 


•z^5 


•864 


109 


399 


600973 


1082 


1191 


1^99 


1408 


15.17 


1625 


1734 


1843 


I95i 


109 


K. 





I 


2 


3 


4 


5 


6 


7 


8 


9 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 





I 


2 


3 j 4 j 5 


1 6 1 7 ! 8 


1 
9 


JD. 
108 


400 


602060 


2169 


2277 


2386 j 1494 2603 


271 1 j 2819 1 2928 


3o36 


401 


3i44 


3253 


336i 


3469 


3577 ; 3686 


3794 


3902 ! 4010 


4118 


108 


402 


4226 


4334 


4442 


455o 


4658 ' 4766 


4874 


4982 ; 5089 1 5197 


1 io8 


4o3 


53o5 


54i3 


5521 


5623 


5736 ; 5844 


•5931 


bo59 i 6166 


6274 


108 


404 


63Si 


6489 


6596 


6704 


681 1 i 6919 


7026 


7'33 , 7241 


7348 


107 


4o5 


-7455 


7062 


7669 


7777 


7884 i 7991 
8954 9061 


8098 ! 8205 j 83i2 


8419 


107 


406 


8526 


8633 


8740 


8847 


9167 


9274 1 9381 


9488 


107 


407 


9594 


9701 


9808 


9914 


••21 j •128 


•234 


•341 1 '447 


•554 


1 ro7 


408 


61066c 


0161 


0873 


0979 


1086 1192 


1 1298 


i4o5 


i5ii 


1617 
2678 


1 106 


409 


1723 


1S29 


1936 


2042 


2148 


2254 


236o 


2466 


2572 


106 


410 


6r^784 


2890 


2996 


3l02 


3207 


33i3 


3419 


3525 


363u 


3736 


106 


411 


3842 


3947 


4o53 


41 59 


4264 


4370 


4475 


458 1 


4686 


4792 


106 


412 


4897 


5oo3 


5io8 


52i3 i 5319 


5424 


5529 


5634 ' 5740 


5845 


io5 


4i3 


5900 


6o55 


6160 


6265 ' 6370 


6476 


658i 


6686 


6790 


6895 


io5 


414 


7000 


7io5 


7210 
8257 


73i5 


7420 


7525 
8571 


7629 


7734 


7839 
8884 


7943 


io5 


41^) 


8048 


8i53 


8362 


8466 


8676 


8780 


8989 


io5 


416 


9093 


9198 


9302 


9406 


9511 


9615 


9719 


9824 


9928 


••32 


104 


417 


620136 


0240 


o344 


0448 


o552 


o656 


0760 


0864 


0968 


1072 


104 


418 


1176 


1280 


1384 


1488 


1592 


1695 


1799 


1903 


2007 


2110 


104 


419 


2214 


23i8 


2421 


2520 


2628 


2732 


2835 


2939 


3042 


3146 


104 


420 


623249 


3353 


3456 


3559 


3663 


3766 


3869 


3973 


4076 


4179 


io3 


421 


4282 


4385 


4488 


4591 


4695 


4798 


4901 


5004 


5107 


5210 


io3 


422 


53 1 2 


54i5 


55i8 


5621 


5724 


5827 


5929 


6o32 


6i35 


6238 


io3 


423 


6J40 


6443 


6546 


6648 


6751 


6853 


6956 


7o58 


7161 


7263 


io3 


424 


7366 


7468 


7571 
8593 


7673 


7775 


7878 


7980 


8082 


8i85 


8287 


102 


423 


83^9 


8491 


8695 


8797 


8900 


9002 


9104 


9206 


93o3 


102 


426 


9410 


9512 


9613 


97i5 


9817 


9919 


••21 


•123 


•224 


•326 


102 


427 


630428 


o53o 


o63i 


0733 


o835 


0936 


io38 


1 139 


1 241 


i342 


103 


428 


1444 


1 545 


1647 


1748 


1849 


1951 


2052 


2i53 


2255 


2356 


lOi 


429 


2457 


2559 


2660 


2761 


2862 


2963 


3o64 


3i65 


3266 


3367 


101 


43o 


633468 


3569 


3670 


3771 


3872 


3973 


4074 


4175 


4276 


4376 


100 


43 1 


4477 


4578 
5584 


4679 


4779 


48tfo 


4981 


5o8i 


5182 


5283 


5383 


100 


432 


5484 


568d 


57b5 


58d6 


5986 


60S7 


6187 


6287 


6388 


100 


433 


6488 


6588 


6688 


6789 


6889 


6989 


7089 


7189 
8190 


7290 


It 


100 


434 


7490 


7590 


7690 


7790 


7890 


7990 


8090 


8290 


99 


435 


8489 


8589 


86^9 


8789 


8ab8 


89^8 


90t,8 9188 


9287 


9387 


99 


436 


94b6 


9586 


9686 


9783 


9885 


9984 


••84 •i83 


•283 


•382 


99 


437 


640481 


o58i 


0680 


0779 


0879 


0978 


1077 1177 


1276 


1375 


99 


438 


1474 
2465 


1573 


1672 


1771 


1871 


1970 


2069 2168 
3o58 3i56 


2267 


2366 


99 


439 


2563 


2662 


2761 


2860 


2959 


3255 


3354 


99 


440 


643453 


3551 


365o 


3749 


3847 


3946 


4044 4143 


4242 


4340 


98 


441 


4439 


4537 


4636 


4734 


4832 


4931 


5029 1 5127 


5226 


5324 


98 


442 


5422 


5521 


56i9 


5717 


58iD 


5913 


6011 1 6110 


6208 


63o6 


98 


443 


6404 


65o2 


6600 


6698 


6796 


6594 


6992 1 7089 


7187 


7285 


98 


444 


7383 


7481 


7579 


7676 


7774 


7872 
8848 


7969 8067 


8i65 


8262 


98 


445 


8360 


8458 


8555 


8653 8730 


8945 9043 


9140 


9237 


97 


1 446 


9335 


9432 


953o 


9627 


9724 


9821 


9919 


••16 


•ii3 1 •210 


07 


447 


65o3o8 


o4o5 


0302 


0399 


0696 


0793 


0890 


0987 


1084 


1 181 


97 


448 


1278 


1375 


1472 


1 569 


i6t)6 


1762 


1809 


1956 


2o53 


2i5o 


97 


449 


2246 


2343 


2440 


2536 


2633 


2730 


2826 


2923 


3019 


3ii6 


91 


45o 


653213 


3309 


34o5 


35o2 


3598 


3695 


3791 


3888 


3984 


4o8c 


96 


45i 


4177 


4273 


4369 


4465 


4562 


4658 


4754 


485o 


4946 


5o42 


06 


452 


5i38 


5235 


533 1 


5427 


5523 


5619 


5715 


58io 


5906 


6002 


96 


453 


6098 


6194 


6290 


6386 


6482 


^?77 


6673 


6769 


6864 


6960 


96 


454 


7056 


7i52 


7247 


7343 


7438 


7334 
8488 


7629 


7725 


7820 
8774 


It 


96 


455 


Son 


8107 


8202 


8298 


8393 


8584 


8679 


95 


456 


8965 


9060 


9155 


9230 


9346 


9441 


9536 


963 1 


9726 


9821 


9^ 


& 


9916 


••11 


•106 


•201 


•296 


•391 


•486 . 


•58i 


•676 1 •771 


95 


660865 


0960 


io55 


ii5o 


1245 


1339 


1434 ' 


1529 


1623 . 


1718 


95 


459 

N. 


i8i3 


1907 


2002 


2096 


2191 


22^6 

5 


228o 1 

6 1 


2473 


256q ■■ 


2663 


^1 


_^_ 


I 


2 




.^. 


'11 


' i 


'j>. 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



460 



662758 


2852 


2 


3 


4 


5 


6 


7 


8 


9 


± 


2947 


3o4i 


3i35 


323o 


3324 


3418 


35i2 


454J 


94 


461 


3701 


3795 


3889 


3983 


4078 


4172 


4266 


4360 


4454 


94 


462 


4642 


4736 


483o 


4924 


5oi8 


5lI2 


5206 


5299 


5393 


5487 


94 


463 


558i 


5675 


5769 


5362 


5906 


6o5o 


6143 


6237 


633 1 


6424 


94 


464 


65i8 


6612 


6705 


6799 


6892 


69S6 


7079 


7173 
8106 


7266 


7360 


94 


465 


7453 
8386 


7546 


7640 
8572 


8665 


7826 


792c 


8oi3 


8199 


8293 


93 


466 


8479 


8759 
9689 


8852 


8945 


9038 


9i3i 


9224 


93 


467 
468 


9317 


9410 


95o3 


9596 


97S2 


9875 


9967 


••60 


•i53 


93 


670246 


0339 


043 1 


OJ24 


0617 


0710 


0802 


0895 


09S8 


1080 


93 


469 


1173 


1265 


i353 


I45i 


1 543 


i636 


1728 


1821 


1913 


2005 


93 


470 


672098 


2190 


2283 


2375 


2467 


256o 


2652 


2744 


2836 


2929 


92! 


4^1 


3021 


3ii3 


32o5 


3297 


3390 


3482 


3574 


3666 


3758 


385o 


92 


/i7i 


itr, 


4034 


4126 


421S 


43io 


4402 


4494 


4586 


4677 


4769 


92 


4^3 


4953 


5o45 


5i37 


5228 


5320 


5412 


55o3 


5595 


5687 


92 


474 


ut. 


5870 


5962 


6o53 


6145 


6236 


6328 


6419 


65ii 


6602 


92 


475 


6785 


6876 


6q68 


7059 


7.5i 


7242 


7333 


7424 


7516 


91 


476 


7607 


til 


77^9 


7881 


7972 


8o63 


8i54 


8245 


8336 


8427 


9» 


477 


85i8 


8700 


8791 


8882 


8973 


9064 


9155 


9246 


9337 


91 


47^ 


9428 


9519 


9610 


9700 


9791 


9882 


9973 


••63 


•I 54 


•245 


91 


479 


68o336 


0426 


o5i7 


0607 


0698 


0789 


0879 


0970 


1060 


ii5i 


9» 


480 


681 241 


i332 


1422 


i5i3 


i6o3 


1693 


1784 


1874 


1964 


2o55 


90 


4S1 


2145 


2235 


2326 


2416 


25o6 


2596 


26S6 


2777 


2867 


2957 


90 


482 


3047 


3i37 


3227 


3317 


3407 


3497 


3587 


3677 


3-67 


3857 


90 


483 


3947 


4037 


4127 


4217 


4307 


4396 


4486 


4576 


4666 


4736 


90 


484 


4845 


4935 


5o25 


5iu 


5204 


5294 
6189 


53S3 


5473 


5563 


5652 


90 


485 


5742 


5o3i 


5921 


6010 


6100 


6279 


6368 


6458 


6547 


89 


486 


6636 


6726 


68i5 


6904 


6994 


7o83 


8064 


7261 


735i 


7440 


89 


ill 


7529 


7618 


7707 


7796 


7886 


797? 


8i53 


8242 


833 1 


89 


8420 


85o9 


8398 


8607 


8776 


8863 


8q53 
9841 


9042 


9i3i 


Q220 


89 


489- 


9309 


9398 


9486 


9575 


9664 


9753 


9930 


••19 


•107 


89 


490 


690196 


0285 


0373 


0462 


o55o 


0639 


0728 


0816 


0905 


0993 


tl 


491 


1081 


1170 


1258 


1347 


1435 


i524 


1612 


1700 


1789 


1877 


492 


■It^ 


2O03 


2142 


223o 


23i8 


2406 


2494 


2583 


2671 


2759 


88 


493 


Itl 


3o23 


3iii 


3199 


3287 


3375 


3463 


355i 


3639 


88 


494 


3727 


3903 


3991 


4078 


4166 


4254 


4342 


443o 


4517 


8S 


495 


46o5 


4693 


4781 


4b68 


4936 


5o44 


5.3i 


5219 


5307 


5394 


881 


496 


5482 


5569 


5607 


5744 


5832 


5919 


6007 


6094 


6182 


6269 


87 


497 


6356 


6444 


653 1 


6618 


6706 


6793 


68S0 


6968 


7o55 


7142 


87 


498 


7229 


7^'7 


7404 


7491 


7578 


7660 


7752 


7839 
8709 


7926 


8014 


87 


499 




8188 


8275 


8362 


8449 


8535 


8622 


8796 


8883 


87 


5oo 


698970 


9057 


9144 


9231 


9317 


9404 


9491 


9578 


9664 


975i 


?' 


5oi 


9^38 


9924 


••11 


••98 


•184 


•271 


•333 


•444 


•53 1 


•617 


87 


502 


700704 


0790 


0877 


0963 


io5o 


ii36 


1222 


i3o9 


1395 


1482 


86 


5o3 


1 568 


16^4 


1741 


1827 


1913 


1999 


2086 


2172 


2258 


2344 


86 


5o4 


243 1 


25i7 


2603 


2689 


2775 


2861 


2947 


3o33 


3119 


32o5 


86 


5o5 


3291 


3377 


3463 


3549 


3635 


3721 


38o7 


3893 


3q^9 


4o65 


86 


5o6 


4i5i 


4236 


4322 


4408 


4494 


4579 


4665 


475i 


4837 


4922 


86 


507 


5oo8 


5094 


5179 


5265 


5350 


5436 


5522 


5607 


5693 


5778 


86 


5o8 


5864 


5949 


6o35 


6120 


6206 


6291 


6376 


6462 


6547 


6632 


85 


509 


6718 


68o3 


6888 


6974 


7059 


7144 


7229 


73i5 


7400 


7485 


85 


5io 


707570 
8421 


7655 


7740 


7826 


791 1 


7996 


8081 


8166 


825i 


8336 


85 


5ii 


85o6 


8591 


8676 


8761 


8846 


8931 


9015 


9100 


9185 


85 


D12 


9270 


9355 


9440 


9024 


9609 


9694 


9779 


9863 


9948 


••33 


85 


5i3 


710117 


0202 


0287 


0371 


0456 


0540 


0625 


0710 


0794 


.0879 
1723 


85 


5i4 


0963 
1807 


1048 


Il32 


1217 


i3oi 


1385 


1470 


1 554 


1639 


84 1 


5i5 


1892 


1976 


2060 


2144 


2229 


23i3 


2397 


2481 


2566 


84} 


5i6 


265o 


2734 


2818 


2902 


2986 
3826 


3070 


3i54 


3238 


3323 


3407 


84! 


5i7 
5i8 


3491 


3575 


3659 


3742 


3910 


3994 


4078 


4162 


4^46 


84 


433o 


4414 


4497 


458 1 


4665 


4749 


4833 


4916 


5ooo 


5o84 


84 


519 


5167 



525i 


5335 


5418 


55o2 


5586 


5669 


5753 


5836 


5930 


84 
D. 


1 


2 


3 


4 


5 


6 


7 


8 


9 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N, 





I 2 


3 


4 


5 


6 


7 1 8 


9 


83 


520 


716003 


6087 


6170 


6254 


6337 


6421 


65o4 


6588 


6671 


6754 


521 


6838 


6921 


7004 


7088 


8oo3 


7254 


7338 


7421 
8253 


7504 
8336 


7587 
8419 
9248 


83 


522 


7671 


7754 


7837 

8668 


7920 


8086 


8169 


83 


523 


b5o2 


8585 


8751 


8834 


8917 


9000 


9083 


9165 


83 


524 


9331 


9414 


9497 


9580 


9663 


9745 


9828 


991 1 


9994 


••77 


83 


520 


720J59, 0242 


o325 


0407 


0490 


0573 


o655 


0738 


0821 


0903 


83! 


526 


0986 


io63 


ii5i 


1233 


i3i6 


1398 


1481 


i563 


1646 


1728 


82 


527 


1811 


1S93 


1975 


2o58 


2140 


2222 


23o5 


2387 


2469 


2552 


82 


528 


2634 


27.6 


2798 


2881 


2963 


3045 


3127 


3209 


3291 


3374 


8a 


529 


3456 


3538 


3620 


3702 


3784 


3866 


3948 


4o3o 


4112 


4194 


82 


53o 


724276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


4931 


5oi3 


82 


53 1 


5095 


5176 


5258 


5340 


5422 


55o3 


5585 


5667 
6483 


5748 


5830 


82 


532 


5912 


5993 


6075 


6i56 


6238 


6320 


6401 


6564 


6646 


82 


533 


6727 


6809 


6890 


6972 


7053 


7134 


7216 


7297 
8110 


7379 


7460 


81 


• 534 


7341 


7623 
8435 


7704 


7735 


7866 
8678 


7948 


8029 


8191 


8273 


81 


535 


8354 


85i6 


8597 


8759 


8841 


8922 


90o3 


9084 


81 


536 


9i65 


9246 


9327 


9408 


9489 


9570 


965i 


9732 


9813 


9893 


81 


537 


9974 


••55 


•i36 


•217 


•298 


•378 


•459 


•540 


•621 


•702 


81 


538 


730782 


o863 


0944 


1024 


iio5 


u86 


1266 


i347 


1428 


i5o8 


81 


539 


1589 


1669 


1750 


i83o 


1911 


1991 


2072 


2l52 


2233 


23i3 


81 


540 


732394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 


3o37 


3117 


80 


541 


3197 


3278 


3358 


3438 


35i8 


3598 


3679 


3759 


3839 


3919 


80 


542 


3999 


4079 


4160 


4240 


4320 


4400 


4480 


456o 


4640 


4720 


80 


543 


4800 


4880 


4960 


5o4o 


5l20 


5200 


5279 


5359 


5439 


55i9 


80 


544 


5599 


5679 


5709 


5838 


5918 


5998 


6078 


6157 


6237 


63i7 


80 


545 


6397 


6476 


6556 


6635 


6715 


6795 


6874 


6954 


7034 


7ii3 


80 


546 


7193 


7272 


7352 


7431 


75ii 


8384 


7670 


U$ 


7829 


7908 


79 


547 


1% 


8067 


8146 


8225 


83o5 


8463 


8622 


8701 


79 


548 


8860 


8939 


9018 


9097 


9177 


9256 


9335 


9414 


9493 


79 


549 


9572 


965i 


9731 


98x0^ 


9889 


9968 


••47 


•126 


•205 


^284 


79 


55o 


740363 


0442 


052I 


0600 


0678 


0757 


o836 


0915 


0994 


1073 


79 


55i 


1132 


I23o 


1 309 


i388 


1467 


1546 


1624 


1703 


178-2 


i860 


79 


552 


1939 


2018 


2096 


2175 


2254 


2332 


241 1 


2489 


2368 


2647 


?^ 


553 


2725 


2804 


2882 


2961 


3o39 


3ii8 


3196 


3275 


3353 


3431 


554 


3510 


3588 


3667 


3745 


3823 


3902 


3980 


4o58 


4i36 


42i5 


78 


555 


4293 


4371 


4449 


4528 


4606 


4684 


4762 


4840 


4919 


4997 


78 


556 


5075 


5i53 


523i 


5309 


5387 


5465 


5543 


5621 


5699 


5777 


78 


557 


5855 


5933 


601 1 


6089 


6167 


6245 


6323 


6401 


6479 


6556 


78 


558 


6634 


6712 


6790 


6868 


6945 


7023 


7101 


7'79 


7256 
8a33 


7334 


78 


559 


7412 


7489 


7567 


7645 


7722 


7800 


7878 


7903 


8110 


78 


56o 


748188 


8266 


8343 


8421 


8498 


8576 


8653 


8731 


8808 


8885 


77 


56 1 


8963 


9040 


9118 


9195 


9272 


9350 


9427 


9504 


9582 


9659 


77 


562 


9736 


9814 


9891 


9968 


••45 


•123 


•200 


•277 


•354 


•43 1 


77 


563 


75o5o8 


o586 


0663 


0740 


0817 


0894 


0971 


1048 


II25 


1202 


77 


564 


1279 
2048 


1 356 


1433 


i5io 


i587 


1664 


1741 


1818 


1895 
2663 


1972 


77 


565 


2125 


2202 


2279 


2356 


2433 


2 509 


2586 


2740 


77 


566 


2816 


2893 


3?]6 


3o47 


3.23 


3200 


3277 


3353 


343o 


35o6 


77 


567 


3583 


366o 


38i3 


3889 


3966 


4042 


4119 


4195 


4272 


77 


568 


4348 


4425 


45oi 


4578 


4654 


4730 


4807 


4883 


4960 


5o36 


76 


569 


5lI2 


5189 


5265 


5341 


5417 


5494 


5570 


5646 


5722 


5799 


76 


570 


755875 


5951 


z°^J 


6io3 


6180 


6256 


6332 


6408 


6484 


656o 


76 


571 


6636 


6712 


6788 


6864 


6940 


7016 


7092 


7168 


7244 


7320 


76 


572 


7396 


nil 


l^^i 


7624 
8382 


7700 


7775 


785i 


7927 


8oo3 


8079 


76 


573 


8i55 


83o6 


8458 


8533 


8609 


8685 


8761 
9517 


8836 


76 


54 


89,2 


8988 


9063 


9139 


9214 


9290 


9366 


9441 


9592 


76 


575 


9668 9743 


98.9 


9894 


9970 


••45 


•121 


•196 


•272 


•347 


75 


576 


760422 


0498 


0373 


0649 


0724 


0799 


0875 


0930 


1025 


XIOI 


'^\ 


577 


1 176 


I25l 


i326 


1402 


1477 


i552 


1627 
2378 


1702 


1778 


1 853 


75 


578 


1928 2oo3 


2078 


2i53 


2228 


23o3 


2453 


2529 

3278 


2604 


75 


579 


2679I 2754 


2829 


2904 


2978 


3o53 


3i28 


32o3 


3353 


75 


N. 





I 


3 


3 


4 


5 


6 


7 


8 


9 


D. 



10 



A TABLE OF LOOARITHMS FROM L TO 10,000. 



1 N. 


1 ° 


I 


' 2 


3 

3653 


1 A 


5 


6 


i 7 


8 


9 


1 1>. 


5So 


763428 35o3 3578 


' 3727 38o2 


3877 


, 3902 


4027 4101 


1 75 


i^' 


4176 4201 4326 


4400 ; 4475. 4300 


4624 


1 4099 


4774 , 4848 


' 75 


! 582 


4Q23' 499S 5072 


5i47 1 5221 5296 


5370 


5445 


1 5)20 5594 


1 75 


1 583 


) 5609 ! ^743 58 1 8 


5892 1 5966 6041 


6ii5 


6190 


6264 6338 


' 74 


! 58/. 


1 6413 6487 6562 


6636 ^ 6710 I 6785 


6859 


6933 


7007 ' 7082 


74 


1 585 


1 7106 7230 7304 1 7379 ' 7453 ; 7527 


' 7601 


7675 


7749 7«23 


. (4 


586 


1 -jS^Sl 7972 8046 812c , 8194 
j 86381 8712 8786 1 8^00 . 8934 


8268 


8342 


8416 


8490 1 8564 


74 


587 


9008 


9082 


9i56 


9230 c2u3 


74 


588 


9377 


94^1 9525 


9099 


! 9^73 


9746 


' 9820 


9S94 


■9968 , ••42 


: 74 


589 


770115 


0189 ; 0263 


o336 


0410 


0484 


0557 ' o63i 


0705 


0778 


74 


5^0 


770S52 


0926 


0999 


1073 


1 146 


1220 


1293 


1367 


1440 


i5i4 


74 


59. 


1587 


1 66 1 


1734 


1808 


I88I 


1955 


2028 


2102 


2175 


2248 


1 73 


5g2 


2322 


2395 


2468 


2542 


26i5 


2688 


2762 


2S35 


2908 


1 29^' 


73 


593 


3o55 


3128 


3201 


3274 


3348 


3421 


3494 


3567 


3640 


3713 


' 73 


594 


3786 


3860 


3933 


4006 


4079 


4i52 


4225 


4298 


4371 


4444 


73 


595 


4517 


4590 


4663 


4736 


4809 


4882 


1 4q55 


5o28 


5ioo 


5i73 


73 


596 


5246; 5319 


5392 


5465 


5538 


56 10 


5683 


5756 


5829 


5902 


73 


597 


59741 6047 


6120 


6193 


6265 


6338 


6411 


6433 


6556 


6629 


73 


598 


6701 


6774 


6846 


6919 


6992 


7064 


7i3t 


7209 


7282 


8079 


73 


599 


7427 


7499 


7572 


7644 


7717 


7789 


7862 


7934 


8006 


72 


600 


778i5i 


8224 


8296 


8363 


8441 


85i3 


8585 


8658 


8730 


8802 


72 


601 


8874' 8947 


9019 


9091 


9163 


9236 


9308 


9380 


94 J 2 


9324 


! 72 


602 


9596, 9"^9 


9741 


9813 


9:^85 


9957 


••29 1 'SOI 


•'73 


•243 


72 


6o3 


780317} o389 


0461 


0533 


o6oD 


0677 


0749 


0821 


0X93 


0965 


1 72 


604 


io37 1109 


1181 


1253 


1324 


1396 


1468 


1540 


1612 1 1684 


72 


6o5 


1755 1827 


1899 


'971 


2042 


2114 


2186 


2.158 


2329 ' 2401 


72 


606 


2473i 2544 


2616 


2688 


2709 


2531 


2902 


2974 


3o46 


3.17 


72 


607 


3189 3260 


3332 


3403 


3470 


3546 


36i8 


36S9 
44o3 


376. 


3832 


7> 


608 


3904 3975 


4046 


4118 


4189 


4261 


4332 


4473 


4546 


71 


609 


4bi7 


4609 


4760 


483 1 


4902 


4974 


5o45 


5ii6 


5i87 


52J9 


71 


610 


785330 


5401 


5472 


5543 


56i5 


5686 


5757 


5828 


5899 


5970 


71 


611 


6041 


6112 


6i83 


6254 


6325 


6396 


6467 


6538 


6609 


6680 


7» 


6.2 


6751 


6822 


6893 


6964 


7o35 


7.06 


7177 


7248 


7319 


7390 


7» 


1 6i3 


7460 


753i 


7602 


7673 


7744 


7815 


7885 


7956 


8027 


8098 


7» 


614 


8168 


8239 


83 10 


838 1 


8451 


8522 


8593 


8663 


8734 


8804 


7« 


6i5 


8875 


8946 


9016 


9087 


9'57 


9228 


9299 


9369 


9440 


95 10 


7» 


616 


gSSi 


9601 


9722 


9792 


9863 


9933 


•••4 


.••74 


•144 


•2l5 


70 


617 


7902S5 


o356 


0426 


0496 


o567 


0637 


0707 


0778 


0848 


0918 


70 


618 


0988 


1009 


1129 


I '99 


1269 


i34o 


1410 


1480 


i55o 


1620 


70 


619 


169 1 


1761 


i83i 


1901 


1971 


2041 


21U 


2l8l 


2252 


2322 


70 


620 


792392 


2462 


2532 


2602 


2672 


2742 


2812 


2882 


2932 


3022 


70 


621 


3092 


3i62 ' 323i 1 


33oi 


3371 


3441 


35ii 


358i 


365i 


3721 


70 


622 


3790 


3 860 


3930 


4000 


4070 


4.39 


4209 


4279 


4349 


4418 


70 


623 


4488 


4558 


4627 


4697 


4767 


4836 


4906 


4976 


5045 


5. ,5 


70 


624 


5i85 


5234 


5324 


5393 


5463 


5532 


56o2 


5672 


5741 


58 n 


70 


! 62D 


588o 


5949 


6019 


6088 


6.58 


6227 


6297 


6366 


6436 


65c5 


69 


626 


6574 


6644 


67.3 


6782 


6352 


6921 


6990 


7060 


7129 


7198 


69 


627 


7263 7337 7406 1 


7475 


7545 


7614 


-7683 


7752 


7821 


7890 


^9 


628 


7c6o 8029 


8098 


8167 
8858 


8236 


83o5 


8374 


8443 


85i3 


8582 


69 


629 


865 1 


8720 


8789 


8927 


8996 


9065 


9134 


9203 


9272 


69 


63o 


799341 


9409 


9478 


9547 


9616 


9685 


9754 


9323 


9892 9901 


69 


63 1 


800029 0098 


0167 


0235 


o3o5 


0373 


0442 


o5ii 


o58c 1 0648 


69 


632 


0717 0786 


o854 


0923 


0992 


1061 


^'29 


1 198 


1266 1335 


69 


633 


1404 1472 


i54i 


1609 


1678 


1747 


i8i5 


1884 


1932 1 2021 


69 


634 


2089 21 58 


2226 


2295 ■ 2363 ! 


2432 


25oo 


2563 


2637 1 270? 


^ 


635 


2774 2842 


2910 1 2979 3o47 1 


3ii6 


3i84 


3232 1 


3321 1 3389 


636 


3457 


3525 


3594 1 3662 : 3730 ! 


3798 


3867 3935 


4oo3 


4071 


68 


637 


4139 


4208 


4276 ! 4344 4412 i 


4480 


4548 4616 


4685 


4753 


68 


482, 


4889 


4957 5o25 


5093 ! 


5i6i 


r^t 


5297 1 


5365 


5433 


68! 


639 


55oi 


5569 


5637 5705 


5773 1 5841 


5976 ■ 


6044 


6112 


_68j 
D. 


N. 





I 


, 1 3 


4 ; 5 


6 


7 ! 


8 


9 1 





A. TABLE 


OF ] 


LOGARITH.MS FROX 1 


TO 10,000. 


IJ 


N. 


1 1 I 


2 


3 


4 1 5 1 ^ 6 1 7 ' 8 


6700 


68 


640 


806180 6248 


63 16 1 6384 


6451 1 6319 1 6587 


6655 6723 


641 


6858 6926 6994 1 7061 


7129 ' 7197 


7264 


7332 7400 ' lAb-] 


68 


642 


7535 


7603 1 76-»o 7738 
8279 1 8346 1 8414 


7806 j 7873 


7941 


8008 8076 1 8143 


68 


643 


8211 


8481 ' 8549 


8616 


8684 8751 8818 


67 


644 


8886 8953 j 9021 1 9088 


9i56 ' 9223 


9290 


9358 9423 ; 9492 


67 


645 


9060 9627 ! 9694 ! 9762 1 9829 1 9896 


9964 1 ••3 1 1 "V 1 •i63 


67 


646 


810233 o3oo 1 o3o7 1 0434 I o5oi 0569 


c63t) 1 0703 j 0770 


0837 


67 


647 


0904 


0971 1 1039 ' 1106 1 1173 i 1240 


i3o7 1 1374 \ 1441 


i5o8 


67 


648 


ID75 


1642 1 1709 


1776 1843 


1910 


1977 


2044 j 2111 


2178 


67 


649 


2245 


23i2 , 2379 


2443 1 25 1 2 


2379 


2:^46 


2713. 


278c 


2847 


67 


65o 


812913 


2980 


3o4/ 


3114 


3i8i 


3247 


33i4 


338 1 


3448 


35i4 


67 


r,Di 


3581 


3648 


37.4 


3781 


3848 


3914 


3981 


4C48 


41 14 


4181 


67 


65:! 


4248 


43i4 


438i 


4447 


45i4 


458 1 


4047 


4714 


4780 


4847 


67 


653 


49"3 


4980 


5046 


5ii3 


5179 


5246 


53i2 


5378 


5445 


55ii 


66 


654 


5578 


5644 


5711 


5777 


5843 


5910 


5976 


6042 


6109 


6175 


66 


655 


6241 


63o8 


6374 


6440 


65o6 


6573 


6639 


6705 


677 r 


6838 


66 


656 


6904 


6970 


7o36 


7102 


7169 


7235 


7301 


7367 


7433 
8094 


7499 


66 


657 


7565 
8:26 


763i 


7698 


77(>4 


783o 


7896 


7962 


8028 


8100 


66 


658 


8292 


8358 


8424 


8490 


8536 


8022 


8688 


8754 


8820 


66 


659 


8885 


8951 


9017 


9063 


9149 


92i5 


9281 


9346 


9412 


9478 


66 


660 


819544 


9610 


9676 


9741 


9807 


9873 


9939 


•••4 


••70 


•i36 


66 


661 


820201 


0267 


o333 


0399 


0454 


o53o 


0593 


d66i 


0727 


0792 


66 


662 


0858 


0924 


0939 


1035 


1120 


1186 


I25l 


i3i7 


i382 


1448 


66 


663 


i5i4 


ID79 


1645 


1710 


1775 


1841 


1906 


1972 


2037 


2103 


65 


664 


2168 


2233 


2299 


2304 


243o 


2493 


256o 


2626 


2601 


2736 


65 


665 


2822 


2887 


2952 


3oi8 


3o83 


3148 


32i3 


3279 


3344 


3409 


65 


666 


3474 


3539 


36o5 


3070 


3735 


38oo 


3865 


3930 


3996 


4061 


65 


667 


4126 


4I9I 


4256 


4321 


4386 


445 1 


43i6 


458i 


4646 


471 1 


65 


668 


4776 


4841 


4906 


4971 


5o36 


5ioi 


5i66 


523i 


5296 


536i 


65 


669 


5426 


5491 


5556 


5621 


5685 


5751 


58.' 3 


588o 


5945 


6010 


65 


670 


826075 


6140 


• 6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 


65 


671 


6723 


6787 


6852 


69.7 


6981 


7046 


71U 


7175 


7240 


73o3 


65 


672 


7369 


7434 


7499 


7063 


7628 


7692 


7737 


7821 
8467 


7886 


7951 


65 


673 


8oi5 


8080 


8144 


8209 


8273 


8338 


8402 


853 1 


8395 


64 


674 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 


64 


675 


9J04 


9368 


9432 


9497 


956i 


9625 


9690 


9754 


9818 


9882 


64 


676 


9947 


••11 


••75 


•139. 


•204 


•268 


«332 


•396 


•460 


'•525 


64 


677 


83o5b9 


0653 


0717 


0781 


0845 


0909 


0973 


1037 


1102 


1 166 


64 


678 


I23o 


1294 


i358 


1422 


i486 


i55o 


i6i4 


1678 


1742 


1806 


64 


679 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


238i 


2445 


64 


680 


832509 


2573 


2637 


2700 


2764 


2828 


2892' 


2956 


3020 


3oS3 


64 


681 


3147 


32II 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


3721 


64 


682 


3784 


3848 


39.2 


3975 


4o39 


41 o3 


4166 


423o 


4294 


4357 


64 


683 


4421 


4484 


4548 


461 1 


4675 


4739 


4802 


4866 


4929 


4993 


64 


684 


5o56 


5l20 


5i83 


5247 


53 10 


5373 


5437 


55oo 


5564 


5627 


63 


685 


5691 


5754 


58i7 


5881 


5944 
6577 


6007 


6071 


6i34 


6197 


6261 


63 


686 


6J24 


6387 


645 1 


65i4 


6641 


6704 


6767 


6830 


6894 


63 


687 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


75?5 


63 


688 


7588 


7652 


77i5 


7778 


7841 


7904 


7967 


8o3o 


8093 


8i56 


63 


689 


8219 


8282 


8345 


8408 


8471 


8534 


8397 


8660 


8723 


8786 


63 


690 


838849* 8912 


8975 


9o38 


9101 


9164 


92?] 


9289 
9918 


9352 


9413 


63 


691 


9478 9341 


9604 1 9667 


9729 


9792 


9853 


9981 


••43 


63 


692 


840106 0169 


0232 1 0294 


0357 


0420 


0482 


o543 


0608 


0671 


63 


693 


0733 0796 


0859 ; 0921 


0984 


1046 


1 109 


1172 


1234 1297 


63 


694 


1359 1422 


1485 : 1 547 


1610 


1672 


1735 


1797 


i860 i 1922 


63 


693 


1985 2047 


2II0 1 2172 


2235 


3297 


2360 


2422 


2484 


2547 


62 


696 


2609 2672 
3233 3295 


2734 : 2796 2859 


1921 


2983 


3046 


3io8 


3170 


6a 


697 


3357 1 3420 3482 


3544 


36o6 


3669 


3731 


3793 


62 


698 


3855 3918 


3980 1 4042 4104 


4166 


4229 


4291 


4353 


44i5 


62 


699 

N. 


4477 4339 


4601 4664 4726 i 4788 


485o 


4912 


4974 


5o36 


62 


C I 


2 1 3 


4 


5 1 6 I 


^ J 


8 1 9 


1>. 



L2 



A TABLE CF L0GAKITHM3 FROM 1 TO 10,000. 



N. 





I 


2 


3 4 


i ' 


6 


, 1 a 


! 9 
1 5656 


i>- : 


700 


845098I 5 1 60 


5222 


5284 


5346 


5408 


5470 


5532 1 5594 


62 


701 


5718 5780 


5842 


5904 


5966 


6028 


6090 


6i5i 


62i3 1 6275 


52 


702 


6337! 6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 ! 68g4 


62 


703 


6955 


7017 


7079 .1 7141 


7202 


7264 


7326 


7388 


7449 


75ii 


62 


704 


m 


7634 


1 7396 ■ 


! "-'58 


7819 


7881 


-943 


8004 


8066 


812S 


62 


705 


8201 


?3l2 


8374 


8433 


8497 


8539 


8620 


8682 


8743 


62 


706 


88o5 


8866 


8928 


8989 


905 1 


9II2 


9174 


9235 


9297 


9358 


61 


708 


9419 


9481 


9D42 


9604 


9665 


9726 


I 9788 


9849 


99" 


997= 


61 


85oo33 


0095 


01 d6 


0217 


0279 


1 o34o 


1 0401 


0462 


0324 


0585 


6i 


709 


0646 


0707 


0769 


o836 


0891 


0932 


1014 


1075 


ii36 


1197 


61 


710 


851258 


l320 


i38i 


1442 


i5o3 


1 564 


1625 


1686 


1747 


1809 


61 


711 


2480 


iqBl 


1992 


2o53 


2114 


2175 


2236 


2297 


2358 


2419 


61, 


712 


2341 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 


61, 


713 


3090 


3i5o 


32II 


3272 


3333 


3394 


3455 


35i6 


3377 


3637 


61 1 


714 


3698 


3759 


3820 


388i 


3941 


4002 


4o63 


4124 


4i85 


4245 


61; 


7'5 


4306 


4367 


442S 


4488 


4549 


4610 


4670 


473 1 


4792 


4852 


61 


7'6 


4913 


4974 


5o34 


5095 


5i56 


5216 


9277 


5337 


5398 


5459 


61 


r.i 


5519 


558o 


5640 


5-01 


5761 


5822 


5382 


5943 


6oo3 


6064 


61 1 


6124 


6i85 


6245 


63o6 


6366 


6427 


6487 


6348 


66o3 1 666S 


60 


719 


6729 


6789 


6850 


6910 


6970 


703 1 


7091 ^ 


7i52 


7212 


7272 


60I 


720 


857332 


7393 


7453 


75i3 


7574 


7634 


7694 ! 7755 


78i5 


7875 


60; 


721 


7935 


7995 


8o56 


8116 


8176 


8236 


8297 i 8357 


84.7 
9018 


8477 


60 


722 


8537 


8597 


8657 


8718 


8778 


8838 


8898 


8953 


9078 


60 


723 


9i38 


9198 


9258 


9318 


9379 
9978 


9439 


9499 


9559 


9619 


9679 


60 


724 


86^338 


9799 


9859 


99.8 


••38 


••98 


•i58 


•218 ! ^278 


60 


72D 


0398 


0458 


o5i8 


0578 


0637 


0697 


0757 ; 0817 


0877 


60 


726 


oq37 


z 


io56 


1116 


1176 


1236 


1293 


1355 


I4l3 


1475 


60 


]^ 


1 534 


1 654 


1714 


1773 


i833 


1893 
2489 


1952 


2012 


2072 


60 


2l3l 


2I9I 


225l 


23lO 


2370 


243o 


2549 


2608 


2668 


60 


729 


2728 


2787 


2847 


2906 


2966 


3o25 


3o83 


3i44 


3204 


3263 


60, 


730 


863323 


3382 


3442 


35oi 


356i 


3620. 


3680 


3730 


3799 


3853 


59' 


731 


3917 


3977 


4o36 


4096 


4i55 


4214 


42-;4 


4333 


4392 


4452 


59, 


732 


401 1 


4070 


463o 


4689 


4748 


4808 


4867 


4926 


4985 


5045 


59 


733 


5io4 


5i63 


5222 


5282 


5341 


5400 


5459 


5319 5578 


5637 
6228 


5o' 


734 


1% 


5755 


58i4 


5874 


5933 


5992 


6o5i 


6110 


6169 


5^' 


735 


6346 


64o5 


6465 


6524 


6583 


6642 


6701 


6760 


6819 


59 


736 


6878 


6937 


6996 


7055 


7114 


7173 


7232 


-1/-W1 


7350 


7409 


59 


737 


7467 


7526 


7083 
8174 


7644 


7703 


7762 


7821 


7S80 


7939 


59 


738 


8o56 


8ii5 


8233 


8292 


835o 


8409 


846S 


8327 


59 


739 


8644 


8703 


8762 


8821 


8879 


8938 


8997 


9o56 


9114 


9173 


59, 


740 


869232 


9290 


9349 


9408 


9466 


9525 


9584 


9642 


9701 


9760 


59 


741 


9818 


9S77 


9935 


9994 


••53 


•hi 


•170 


•22S 


•287 


•345 


1^ 


742 


870404 


0462 


0021 


0579 


0638 


1^', 


0755 ) 


oSi3 


0872 


0930 


743 


0989 


1047 


1106 


Ii64 


1223 


i339 j 


1398 


1456 


13l5 


58 1 


744 


ID73 


i63i 


1690 


1748 


1806 


1 865 


1923 


19S1 


2040 


2098 
2681 


58! 


745 


2i56 


22l5 


2273 


233 1 


23.S9 


2448 


25o6 i 


2554 


2622 


58: 


746 


2739 


2797 


2855 


2913 


2972 


3o3o 


3o88 : 


3.46 


3204 


3262 


58; 


?s 


3321 


33?9 


3437 


3495 


3553 


36ii 


3669 i 


2127 


3785 


3844 


58, 


3902 


3960 


4018 


4076 


4i34 


4192 


425o 


43o8 


4366 


4424 


581 


749 


4482 


4540 


4598 I 


4656 


4714 


4772 


4830 


488S 


4y45 


5oo3 


581 


750 


875061 


5ii9 
5698 


5.77 


5235 


5293 


535i 


5409 


5466 


5524 


5582 


58 1 


75i 


5640 


5756 


53 1 3 


5871 


5929 5987 1 


6045 


6102 


6160 


58 


752 


621 8 


6276 


5333 


6391 


6449 


65o7 


6564 


6622 


6680 


6737 


581 


753 


6795 


6853 


6910 


6968 i 


7026 


70S3 


7141 


7199 


7256 1 


73U 


58; 


734 


7371 


T429 


7487 


7544 1 


7602 ! 


7639 


7717 


8349 


7832 


z^^^ 


58 j 


755 


7947 


8004 { 


8062 


8119 ! 


8177 i 


8234 ' 8292 1 


8407 


8464 


57! 


756 


8522 


8579 ! 


8b37 


8694 ! 8752 I 


8809 i 8«66 ' 


8924 8981 1 90 J9 


P' 


757 


9096 


9153 


9211 


925s ' 9325 1 


93S3 ! 9440 ' 


9497 ; 93" 9^'? 


57 1 


758 


9669 


9726 


9784 , 9^41 i 9S98 ! 


9956 i ••i3 


••70 ^127 ^183 


^'^i 


N. 


880242 0299 


o356 1 0413 j 0471 


o528 1 o585 j 


0642 j 0699 j 0706 1 


37 i 


' I : 2 : 3 ' 4 ; 


5 ' 6 i 


7 i 8 1 9 


D. 



A TABLE OF LOGARITHMS FEOit 1 TO 10,000. 



13 



760 





I 


2 


3 \ 4 


! 5 i 6 
1 1 


7 


8 


9 


D. 


880814 


0871 


0928 


0985 


1042 


1099 


Ii56 


I2l3 


1271 


i328 


"57 


761 


i385 


1442 


1499 


1 556 


i6i3 


1670 


1727 


1784 


1841 


1898 


57 


762 


1955 


2012 


2069 


2126 


2i83 


2240 


2297 


2354 


241 1 


2468 


57 


763 


2525 


258 1 


2638 


2695 


2702 


2809 


2366 


2923 


2980 


3o37 


57 


764 


3093 


3i5o 


3207 


3264 


3321 


3377 


3434 


3491 


3548 


36o5 


57 


765 


366 1 


3718 


3775 


3832 


3888 


3945 


4002 


4C39 


4ii5 


4172 


37 


766 


4229 


4285 


4342 


4399 


4455 


45i2 


4569 


4625 


4682 


4739 


57 


767 


4795 


4852 


4909 


4960 


5o22 


5078 


5i35 


0192 


5248 


5303 


57 


768 


536 1 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


58i3 


5870 


U 


769 


5926 


5983 


6039 


6096 


6i52 


6209 


6265 


6321 


6378 ) 6434 


770 


S86491 


6547 


6604 


6660 


6716 


^1^1 


6829 


6885 


6942 


6998 


56 


771 


7054 


7111 


7167 


7223 


7280 


7336 


7392 


7449 


7303 


736. 


56 


772 


7617 


7674 


773o 


77S6 


7842 


7898 
8460 


7935 


8011 


8067 


8123 


56 


773 


8179 


8236 


8292 


8348 


8404 


85i6 


8573 


8629 


8685 


56 


774 


874. 


8797 


8853 


8909 


8965 


9021 


9077 


9'34 


9190 


9246 


56 


775 


9302 


9358 


0414 


9470 


9526 


9582 


9638 




9730 


9806 


56 


776 


9862 


9918 i 9974 


••3o 


••86 


•141 


•197 


•233 


•309 


•365 


56 


777 


890421 


0477 


o533 


o589 


0645 


0700 


0756 


0812 


0868 


0924 


56 


778 


0980 


io35 


1091 


1 147 


I203 


1259 


i3i4 


1370 


1426 


1482 


56 


779 


1537 


1593 


1649 


1703 


1760 


1816 


1872 


1928 


1983 


2039 


56 


780 


892095 


2i5o 


2206 


2262 


23i7 


2373 


2429 


2484 


2540 


2595 


56 


781 


265i 


2707 


2762 


23i8 


2873 


2929 


2985 


3o4o 


3096 


3:31 


56 


782 


3207 


3262 


33i8 


3373 


3429 


3484 


3 340 


3595 


365i 


3706 


56 


783 


3762 


3817 


3873 


3928 


3984 


4039 


4094 


4130 


42o5 


4261 


55 


784 


43 16 


4371 


4427 


4482 


4533 


4593 


4648 


4704 


4759 


4814 


55 


785 


4870 


4925 


4980 


5o36 


0091 


5146 


5201 


5257 


53i2 


5367 


55 


786 


5423 


5478 


5D33 


5588 


5644 


0699 


5754 


5809 


5864 


5920 


55 


7?7 


5975 


6o3o 


6oS5 


6140 


6195 


6251 


63o6 


636i 


6416 


6471 


55 


788 


6026 


658i 


6636 


6692 


6747 


6802 


6857 


6912 


6967 


7022 


55 


789 


7077 


7i32 


7187 


7242 


7297 


7352 


7407 


7462 


7317 


7372 


55 


790 


897627 


7682 
823i 


& 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


55 


791 


8176 


8341 


8396 


8451 


83o6 


8561 


86i5 


8670 


55 


792 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9:09 


9164 


9218 


55! 


793 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9636 


971 1 


9766 


55 


794 


9821 


9875 


9930 




••39 


••94 


•149 


•203 


•258 


•3l2 


55 


795 


900367 


0422 


0476 


?d3i 


o586 


0640 


0695 


0749 


0804 


0859 


55 


796 


0913 


0968 


1022 


1077 


ii3i 


1186 


1240 


1295 


1349 


1404 


55 


797 


1458 


IDl3 


1 567 


1622 


1676 


1731 


1785 


1840 


1894 


1948 


54 


798 


2oo3 


2037 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 


54 1 


799 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3o36 


54 1 


Boo 


903090 


3i44 


3199 


3253 


3307 


3361 


3416 


3470 


3524 


3578 


541 


3oi 


3633 


3687 


3741 


3795 


3849 


3904 


3953 


4012 


4066 


4120 


54 i 


302 


4174 


4229 


4283 


4337 


4391 


4443 


4499 


4553 


4607 


4661 


541 


3o3 


4716 


4770 


4824 


4878 


4932 


4986 


5o4o 


5094 


5i48 


5202 


541 


804 


5256 


53io 


5364 


5418 


5472 


5526 


558o 


5634 


5688 


5742 


54 


8o5 


5796 


585o 


5904 


5958 


6012 


6066 


6119 
6658 


6173 


6227 


6281 


54; 


806 


6335 


6389 


6443 


6497 


655i 


66o4 


6712 


6766 


6820 


54! 


^ 


6874 


6927 


6981 


7035 


7089 


7143 


7196 


7250 


73o4 


7358 


54 


741 1 


7465 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 
843 1 


54 


809 


7949 


8002 


8o56 


8110 


8i63 


8217 


8270 


8324 


8378 


54 


810 


908485 


8539 


8592 


8646 


8699 


8753 


8807 


8860 


8914 


8967 


54 


811 


9021 


9074 


9128 


9181 


9235 


9589 


9342 


9396 


9449 


95o3 


54 


812 


9556 


9610 


9663 


9716 


9770 


9823 


9877 


9930 


9984 


••37 


53 


8i3 


910091 


0144 


0197 


025l 


o3o4 


o358 


041 1 


0464 


o5i8 


0571 


53 


814 


0624 


0678 


0731 


0784 


o838 


0891 


0944 


0998 


io5i 


1 104 


53 


8i5 


ii58 


1211 


1264 


i3i7 


137. 


1424 


1477 


1 530 


i584 


1 637 


53 


816 


1690 


1743 


1797 


i85o 


1903 


1956 


2009 


2o63 


2116 


2169 


53 


817 
818 


2222 


2275 


2328 


238i 


2435 


2488 


2541 


2594 


2647 
3178 


2700 


53 


2753 


2806 


2859 


2913 2966 


3019 


3072 


3i25 


3231 


53 


819 


J284 


3337 


3390 


3443 I 3496 


3549 


36o2 


3655 


3708 


3761 


53 


N. 


__°_ 


I 


2 


3 ! 4 


5 


6 


7 


8 


9 


D. 



14 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


1 I 1 2 


3 


4 i 5 


6 


7 


8 


1 9 




820 


9i38i4 3867 ; 392c 


1 3975 


4026 


4079 


4i32 


4184 


4237 


4290 


53 


821 


4343 4396 4449 


1 45o2 


4555 


4608 


4660 


4713 


4766 


48.9 


53 


822 


4872 4925 4977 


1 5o3o 


5o83 5i36 


5189 


5241 


5294 


5347 


53 


823 


5400 5453 ' 55o5 


5558 


56ii 


5664 


5716 


5769 


5822 


5»75 


53 


824 


5927 59S0 1 6o33 


6ob5 


6i38 


6191 


6243 


6296 


6349 


6401 


53 


825 


6454 65o7 6559 


66i2 


6664 


6717 


6770 


6822 


6875 


6927 


:-3 


826 


6960 7033 ' 7ob5 


7.38 


7190 


7243 


7295 


7348 


7400 


7453 


531 


827 


7506 7558 761 1 


7663 


7716 


7768 


7820 


7873 


7925 


7978 


5^ 


828 


8o3o 8o83 ' 81 35 


8 188 


8240 


8293 


8345 


8397 


8450 


85o2 


52 


829 


8355 8607 1 8659 


8712 1 8764 


8816 


8869 


8921 


8973 


9026 


52 


83o 


919078 9i3o 9183 


9235 1 9287 


9340 


9392 


9444 


9496 


9549 


52 


83 1 


9601 9653 9706 


9758 ^ qbio 


9862 


9914 


9967 


••19 


••71 


•52 


832 


920123, 0176 0228 


0280 1 o332 


o384 1 0436 


0489 


054. 


0593 


52 


833 


06^5 0697 


0749 


0801 1 o653 


0906 


0908 


1010 


.062 


:ii4 


52 


834 


1 1 66 1 2 1 8 


1270 


l322 


i374 


1426 


1478 


i53o 


.582 


i634 


52 


835 


1 686 1738 


1790 


1842 


■1894 


:946 


1998 


2o5o 


2.02 


2.54 


52 


836 


2206: 2258 


2310 


2362 


2414 


2466 


25i8 


2570 


2622 


2674 


52 


837 


2725' 2777 


2529 


2d8i 


2933 


2985 


3o37 


3089 


3 140 


3.92 


52 


838 


3244 3296 


3348 


3399 


3451 


35o3 


3555 


3607 


3658 


3710 


52 


839 


3762, 3Hi4 


3865 


3917 


3969 


4021 


4072 


4124 


4176 


4228 


52 


840 


924279 433i 


4383 


4434 


4486 


4538 


4589 


4641 


4693 


4744 


52 


841 


479^ 4848 


4«99 


4951 


5oo3 


5o54 


5io6 


5i57 


5209 


5261 


02 


842 


53i2| 5364 


5410 


5467 


55i8 


5570 


5621 


5673 


5725 


5776 


52 


843 


3028; 5b79 


5931 


0902 j 6o34 


6ob5 


6137 


6i88 


6240 


6291 


5i 


844 


6342' 6394 


6445 


6497 6548 


6600 


665 1 


6702 


6754 


6bo5 


5i 


845 


6bJ7 6908 


6959 


7011 7062 


7114 


7i65 


7216 


7268 


73.9 


5i 


846 


7370 7422 


7473 


7524 ! 7576 


7627 


7678 


7730 


7781 


7832 
8345 


5i 


847 


7bt)3 7935 


7986 


8037 


8o»8 


8140 


9191 


8242 


8293 


5i 


848 


8396 8447 


8498 


8549 


8601 


8652 


8703 


8754 


88o5 


8857 


5i! 


849 


89081 8959 


9010 


906*1 


9112 


9163 


92i5 


9266 


93.7 


9368 


5i| 


85o 


929419" 9470 


9521 


9572 


9623 


9674 


97.25 


9776 


9827 


9879 


5ii 


85 1 


9y3o 9981 


••32 


••63 


•i34 


•i85 


•236 


•287 


•33S 


•389 


5i 


852 


930440 1 0491 


o542 


0592 


0643 


0694 


0745 


0796 


0847 


0898 


i'\ 


853 


0949 1000 


io5i 


1102 


1153 


1204 


1254 


l30D 


.356 


1407 


5i 


854 


1458 1 509 


i56o 


1610 


1661 


1712 


1763 


1814 


1865 


1915 


5i 


855 


1906 2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 


5i 


856 


2474 2524 


2575 


2026 


2677 


2727 


2778 


2829 


^^^> 


2930 


5i 


857 


2981 3o3i 


3o«2 


3i33 


3i83 


3234 


3285 


3335 


3386 


3437 


5i 


858 


3487 3538 


3589 


3039 


3690 


3740 


3791 


3841 


3»92 


J943 


5i 


859 


3993 1 4044 


■4094 


4145 


4.95 


4246 


4296 


4347 


4397 


4448 


5i 


860 


934498 1 4549 


4599 


4650 


4700 


4731 


4801 


4852 


4002 


4953 


5o 


861 


5oo3, 5o54 


5io4 


5i54 


52o5 


5255 


53 06 


5356 


5406 


5457 


5o 


862 


5oo7; 5558 


56o8 


5658 


5709 


5759 


5809 


5860 


5910 


5960 


^ 


863 


6011 6061 


6!I1 


6162 


6212 


6262 


63i3 


6363 


64.3 


6463 


5o 


864 


65 14 6564 


6614 


6665 


6715 


6765 


68i5 


6865 


6916 


6966 


5o 


865 


7016 7066 


7117 


7167 


7217 


7267 


7317 


7367 


7418 


7468 


5o 


866 


7518 7568 
8019 8069 


7618 


7668 7718 


7769 


& 


7869 


79'9 


7969 


5o 


867 


8,19 


6169 ; 8219 


8269 


8370 


8420 


S470 


5o 


863 


8520 8570 


8620 


8670 8720 


8770 


8820 


G870 


8920 


8970 


5o! 


869 


9020| 9070 


9120 


9,70 


9220 


9270 


9320 


9369 


9419 


9469 


5o 


870 


939519 9569 


9619 


9669 


9719 


9769 


98.9 


9869 


9918 


9968 


r\ 


871 


940018 006S 


ou8 


0168 1 02l8 


0267 


o3i7 


o367 


0417 


0-,67 


^° 


872 


o5i6 o566 


0616 


0666 i 0716 


0765 


o8i5 


o865 


09.5 


0964 


5oj 


873 


1014 1064 


1114 


ii63 j I2i3 


1263 


i3i3 


i362 


1412 


1462 


5o' 


84 


i5ii i56i 


1611 


1660 I 1710 


1760 


1809 


1 859 


1909 


1958 


5oi 


875 


2008 2o58 


2107 


2i57 ! 2207 


2256 


23o6 


2355 


24o5 


2455 


5o: 


876 


25o4 2554 


26o3 


2653 1 2702 


2752 


2801 


285 1 


2901 
3396 


2950 


5o 


877 


3ooo 3049 


3099 


3148 ! 3198 


3247 


3297 


3346 


3445 


59^ 


878 


3495 3544 


3593 


3643 ; 3592 


3742 1 3791 


3841 


3.S90 


3q3Q 


do; 


879 


3989 4o38 


4088 


4137 1 4186 


.4236 i 4285 


4335 


43«4 


4433 


59 


N. 


j I 


a 


3 i 4 


5 i 6 


7 


8 


^ 


D.\ 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



15 



1 N. 





I 1 2 


3 4 I 3 


6 


7 


8 


9 


D. 
49 


8So 


944483 


, 4532 1 45Si 


463 1 ! 4680 1 4729 


4779 


4828 


|4877 


4927 


88 1 


4976 


' 3025 3074 


3124 


5173 


5222 


1 5272 


5321 


5370 


5419 


49 


882 


546g 


'5518 5567 


i 56i6 


5665 


5715 


1 3764 


5^13 


3662 


5912 


49 


883 


596, 


60 1 c 6009 


6io3 I 6157 


6207 


6256 


63o5 


6354 


6.io3 


49 


884 


• 6432 


■ 6301 ' 655i 


6600 j 6649 


6698 


6747 


6796 


6845 


6894 


49 


885 


i 6943 


: 6992 1 704 t 


7090 7140 


7189 


7233 


7287 1 7336 


7335 


1 49 


886 


1 7434 


' 74&3 i 7532 


75ai 763o 


7679 


7723 


7777 1 7^26 


7873 


1 49 


887 


! 7924 

! 8413 


i 7973 8022 


] 8070 81 19 


8i63 


8217 


8266 83 1 5 1 8364 


1 49 


888 


8462 85 1 1 


856o [ 8609 


8657 


1 8706 


8755 : S804 


8853 


I 49 


889 


i 8902 


8931 ; 8999 


1 9^48 j 9097 


J146 ' 9195 


, 9244 


9292 


[ 9341 


49 


890 


949390 


9439 ' 9488 


gojo 9585 


9634 


9683 


9731 


9780 


9829 


49 


891 


9376 


9926 9975 


••24 


••73 


•121 


•170 


•219 


•267 


•3i6 


49 


892 


930.J63 


0414 0462 


o5ii 


o56o 


0608 


o657 


0706 


0754 


o-.o3 


49 


893 


0001 


0900 0949 i 0997 


1046 


1093 


1143 


1192 


1240 


1289 


49 


894 


i338 


i386 1435 14^3 


i532 


i5:io 


1629 


1677 


1726 


1775 


it 


895 


lb23 


1872 IQ20 1 1969 


20IT 


2066 


2II4 


2i63 


2211 


2260 


896 


23oti 


2356 2403 ! 2433 


25o2 


255o 


2599 


2647 


2096 


2744 


48 


897 


2792 


2841 2839 


2933 


2986 


3o34 


3os3 


3i3i 


3i8o 


3228 


48 


898 


3276 


3325 3373 


342. 


3470 


35i8 


3566 


36i5 


3663 


37.1 


48 


899 


3700 


3do8 3856 


3905 


3953 


4001 


4049 


; 4098 


4146 


4194 


48 


900 


904243 


4291 4339 


4387 


4435 


4484 


4532 


' 458o 


4628 


4677 


48 


901 


4723 


4773 4821 


4809 


4918 


4966 


5oi4 


5o62 


5iio 


5i58 


48 


902 


D207 


5255 53o3 


535, 


5399 


5447 


5495 


5543 


5592 


5b4o 


48 


903 


5o»8 


5735 5784 1 5o32 


SSdo 


5928 


5976 


6024 


6072 


6120 


48 


904 


6i6d 


6216 6265 I 63 1 3 


6361 


6409 


6457 


65o5 


6553 


6601 


48 


905. 


60^9 


6697 6745 1 6793 1 


6846 


68^8 


6936 


6934 


7082 


7080 


48 


^06 


7120 


7176 7224 


7272 


7320 


7363 


7416 


7464 


7512. 


7339 


48 


907 


7007 


7655 7703 


7731 


7799 


7847 


7894 


7942 


7990 


8o33 


48 


908 


8006 


8i34 8181 


8229 


8277 


8325 


8373 


8421 


8406 


85i6 


48 


909 


8564 


8612 8659 8707 


8755 


88o3 


885o 


&898 


8946 


8994 


48 


910 


939041 


90S9 9137 9i85 


9232 


9280 


9328 


9375 


9423 


9471 


48 


911 


9018 


9566 9614 9561 


9709 


9737 


9804 


9S52 


9900 


9947 


48 


912 


9^93 


••42 ••90 


•i33 


•183 


•233 


•2iO 


•323 


•J7& 


•423 


48 


913 


9^0^71 


03 1 8 o566 


06.3 


0661 


0709 


0706 


0S04 


o35i 


o«99 


48 


914 


09-^6 


0994 1 04 1 


1089 


Ii36 


1184 


123l 


1279 


i326 


1374 


47 


li5 


1421 


1469 i5i6 1 i563 1 


1611 


i658 


1706 


1753 


1801 


1848 


47 


916 


1693 


1943 1990 


203S 


2o85 


2l32 


2i3o 


2227 


2275 


232-2 


47 


9n 


2369 
2843 


2417 2464 


25n 


2559 


2606 


2653 


2701 


2748 


2795 


47 


918 


2890 ; 2937 


2985 


3o32 


3079 


3i26 


3i74 


3221 


3268 


47 


919 


33i6 


3363 . 3410 


3457 


35o4 


3552 


3599 


3646 


3693 


3741 


47 


920 


963788 


3835 ' 3882 


3929 


3977 


4024 


4071 


41 18 


41 65 


4212 


47 


921 


4260 


4307 ! 4354 4401 1 


4448 


4493 


4542 


4590 


4637 


4684 


47 


922 


4731 


4778 ■ 4825 


4872 1 


4919 


4966. 


5oi3 


5o6i 


5io3 


5.55 


47 


923 


3202 


5249 ■ 3296 


5343 


5390 


5437 


54^4 


553 1 


5578 


5625 


47 


924 


5672 


3719 ; 5766 


58i3 


5%o 


3907 


3954 


6001 


6048 


6095 


47 


925 


6142 


6189 ; 6236 


62S3 


6329 


6376. 


6423 


6470 


65 17 


6564 


47 


926 


66II 


6658 1 6705 


6752 


6-' 99 


6843 


6.S92 


6939 
74o3 


6986 


7033 


47 


927 
928 


7080 


7127 7173 


7220 


7267 


73i4 


736. 


7454 


7501 


47 


7348 


7595 7642 


7688 


7735 


77S2. 


7829 


7875 


7922 


7969 


47 


r-9 


8016 


8062 8109 


8i56 


8203 


8249 


8296 


8343 


8890 


8436 


47 


930 


08483 


853o • 8576 


8623 


8670 


8716 


8763 


8810 


8856 


8903 


47 


931 


8900 


8996 9043 


9090 


9i36 


9x83: , 9229 


9276 


9823 ' 9369 


47 


^}l 


9416 


9463 , 9309 


9556 


9602 


9649- 9693 


9742 


9789 9^35 


47 


933 


9^82 


9928 9973 


••21 


••63 


•ii4 


•161 


•207 1 


•254 j ^300 


4? 


934 


Q70347 


0893 0440 


0486 


o533 


0379 


0626 


0672 


0719 1 0765 


40 


q3d 


0812 


o853 0904 


0951 0997 


1044 


1090 


1.37 


ii33 j 1229 


46 


936 


1276 


i322 i369 


I4i5 1461 


i5o8 


1 554 


1601 


1647 1693 


46 


9^:^ 


1740 


1786 i i832 


1879 1925 
2342 1 2383 


1 97 1 


20l3 


2064 


2110 2i57 


46 


938 


22o3 


2249 ' 2295 


2434 


2481 


2027 2573 1 2619 


46 


939 


2666 


2712 i 2758 


2804 ! 285i 1 


2897 


2943 


2989 3o35 j 3082 


46 


N. 





I '1 2 j 3 1 4 ! 


5 1 6 


7 


8 


9 1 


I>. 



26 



16 



A TABLE OF LOGARITHMS FKOil 1 TO 10,000. 



K. 



940 

94a 
943 
944 
945 
946 
947 
948 

949 
930 
901 

932 
954 

956 
957 
958 
959 
960 
961 
962 
963 
964 
965 
966 
967 
968 
969 
970 
971 
972 
973 

976 

97J 
979 



982 
9? 
983 
9? 

989 

990 
99« 
99» 
99^ 
994 

996 
997 
998 
999 



973i2d' 0174 

3590' 3636 

403I 4097 

4312 4338 

4972; 5oi8 

5432 5478 
5891 
6330P 
6808} 

7266! 7312 

97T724 .. 

8181 82; 

8637 8683 

9093 9138 

9548 9394 

980003 0049 

0438 o5o3 

0912 0957 

i366 141 1 

1819 1864 

982271; 23i6 
2723 2769 

3175, 3220 

3626 3671 
40771 4122 
4327 4572 
4977 1 0022 
5426 5471 
58751 5920 
6324 6369 

986772! 6817 
7219' 7264 
7666 771 1 
8ii3 8137 
8339 8604 
9003 9049 
9430 94c, 
9<jS; 



991226 
166; 
2III 

255-^ 

345 D 
38" 
43i- - 
475- ^:: 
5196 32^ 

995633 
60-^ 
65i2 

7823 
82>: 

oi3i 
956: 



>:■ 



Uzo 



3220 
3682 
4143 
4604 
5o64 
5324 
5983 
6442 



7358 

7815 
8272 
8728 
9184 
9639 
0094 
o549 
ioo3 
1456 
1909 

2362 

2814 
3265 
3716 
4167 
4617 
5067 
55i6 
5965 
64i3 

6861 
7309 

?I^ 

c:c-. 



3266 
3728 
4189 
465o 
5iio 
5570 
6029 
6488 
6946 
74o3 

7861 
83i7 
9774 
9230 
9685 
0140 
0594 
1048 
i5oi 
1954 

2407 
2859 
33io 



I 9 



33i3 I 33>G 

3774 382 

4235 1 42 

4696 ■- 

3136 

56i6 

60-5 :; 

6533 c; 



■ "- 


3^0- 


3^.3 



• _ - 



- ; -3 



Iir2 



D. 

46 
46 
46 
46 
46 
46 
46 
46 
46 
46 

46 
46 
46 
46 
46 
45 
45 
45 



-3 

_5 

43 
45 
45 
45 
45 
45 



44 

44 
44 
44 

i4 



43 



A TABLE 



OF 



LOGAEITHMIC 
SINES AND TANGENTS 



FOR EVERY 



DEGREE AND MINUTE 
OF THE QUADEANT. 



Eemaek. The minutes in the left-hand column of eacli 
page, increasing downwards, belong to the degrees at the 
top ; and those increasing upwards, in the right-hand column, 
belong to the degrees below. 



18 



(0 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


' Cosine 


D. 


Tang. 


D 





Cor&ng. 


1 


o 






10.000000 




0- 000000 




1 Infinite. 


: 60 


I 


6-463726 


5017.17 


000000 


•00 


6-463726 


5017.17 


13-536274 




2 


764736 


2934-85 


000000 


.00 


764756 


2934 


• 83 


235244 


3 


940H47 


2082.31 


000000 


.00 


940S47 


2082 


-3i 


059153 


57 


4 


7'065786 


1615.17 


000000 


•00 


7.065786 


i6i5 


n 


12-934214 
637304 


56 


s 


162696 


1319-68 


000000 


-00 


162696 


i3i9 
ni5 


^i 


: 55 


6 


241877 


III5-75 


9.999999 


•01 


241878 


758122 


; 54 


I 


308824 


966-53 


999999 


•01 


30.S825 


§?? 


53 


691 175 


i 53 


3668 1 6 


852-54 


999999 


•01 


366817 


54 


633 1 83 


1 52 


9 


417968 


762-63 


999999 
999998 


•01 


417970 


762 


63 


582o3o 


5i 


10 


463725 


689-88 


•01 


463727 


689 


88 


536273 


5o 


II 


7.5o5n8 


629.81 


9.999998 


• 01 


7.505 120 


629 


81 


12-494880 


40 

43 


12 


542906 


579-36 


999997 


•01 


542909 


579 


33 


457091 


i3 


577668 


536-41 


999997 


-01 


577672 


536 


42 


422328 


47 


14 


609853 


499-38 


999996 


-01 


609857 


499 


39 
i5 


390143 


I 46 


i5 


689816 


467.14 


999996 


•01 


639820 


467 


36oi8o 


45 


i6 


667845 


438-81 


999995 


•01 


667H49 


438 


82 


332 i5i 


44 


'I 


694173 


413-72 


999993 


•01 


694179 


4i3 


73 


3o582i 


43 


718997 


391-35 


999994 


•01 


719004 


39, 


36 


280997 


i 42 


•9 


742477 


371-27 


999993 


-01 


742484 


371 


28 


257316 


! 41 


20 


764754 


353-15 


999993 


•01 


764761 


35i 


26 


235239 


40 


21 


7-785943 
806146 


336-72 


9.999992 


•01 


7.785951 


336 


73 


13.214049 
193845 


u 


22 


321.75 


999991 


•01 


806 1 55 


321 


76 


23 


825451 


3o8-oj 


999990 
999980 
999988 


-0] 


825460 


3o8 


06 


174540 


ll 


24 


843934 


itu 


•02 


843944 


295 
283 


49 


i56o56 


25 


861662 


•02 


861674 


90 


138326 


35 


26 


878695 
895085 


273-17 


999988 


•02 


878708 


273 


18 


121292 


34 


27 


263-23 


999987 


• a2 


895099 


263 


25 


104901 


33 


28 


910879 


lloll 


999986 


•02 


& 


254 


01 


089106 
073866 


32 


29 


9261 19 


999985 


•02 


245 


40 


3i 


3o 


. 940842 


237-33 


999983 


•02 


940858 


237 


35 


059142 


3o 


3i 


7-955o82 


229-80 


9.999982 


•02 


7.955100 


229 


81 


12.044900 


li 


32 


968870 


222-73 


999981 


•02 


968889 


222. 


75 


o3iiii 


33 


982233 


216-08 


999980 


•02 


982253 


216. 


10 


017747 


27 


34 


995108 
8.007787 


209-81 
203.90 
198.31 


999979 


•02 


995219 


209 


83 


004781 


26 


35 


999977 
999976 


•02 


8-007809 


2o3 


92 


11-992191 


23 


36 


020021 


•02 


020043 


198 


33 


9-99P5 
968055 


24 


U 


031919 


193-02 


999975 


-02 


031945 




o5 


23 


043 5o I 


I88-OI 


999973 


-02 


043327 


188 


o3 


956473 


22 


2q 


054781 


183-25 


999972 


•02 


054809 


1 83 


27 


945191 


21 


46 


065776 


178-72 


999971 


•02 


o658o6 


178 


74 


934194 


2a 


41 


8 -076500 


174-41 


9.999969 


•02 


8-076531 


174 


44 


11-928469 


\l 


42 


086965 


170-31 


999968 


-02 


0S6997 


170. 


34 


9i3oo3 


43 


097183 


166-39 
162-65 


999966 


•02 


097217 


166. 


42 


^02^83 


n 


44 


107167 


999964 


•o3 


107202 


162- 


68 


8&037 


16 


45 


116926 


159-08 


999963 


•o3 


116963 


159. 


10 


i5 


46 


1 2647 1 


153-66 


999961 


•o3 


i265io 


l53. 


68 


873490 


14 


47 


i358io 


152-38 


999959 
999958 


•o3 


i3585i 


l52. 


41 


864149 


i3 


48 


144953 


149-24 


•o3 


144Q96 
153952 


149- 


27 


855004 


12 


49 


153907 


146-22 


999950 


•o3 


146- 


27 


846048 


11 


5o 


162681 


143.33 


999954 


•o3 


162727 


143- 


36 


837273 


10 


5i 


3-171280 


140-54 


9.999952 


•o3 


8^i7i328 


140- 


57 


11-82S672 


I 


52 


179713 


137-86 


999950 


•03 


179763 
i88o36 


i37- 


T. 


820237 


53 


187985 


135.39 


999948 


•03 


i35. 


81 1964 


I 


54 


196102 


i32.8o 


999946 


.03 


iq6i56 


l32. 


84 


808844 


55 


2040-'0 


130-41 


999944 


.o3 


204126 


i3o. 


44 


795«74 
788047 


5 


56 


liiSoi 


128.10 


999942 


.04 


211953 
219641 


128. 


14 


4 


57 


219581 


125.87 


999940 


.04 


125- 


90 


780359 


3 


58 


227134 


123.72 


999938 


• 04 


227195 


123. 


76 


772803 


2 


59 


234557 


121.64 


999936 


•04 


234621 


121. 


68 


765379 


I. 


66 


241855 


119. 63 


999934 


• 04 


241921 


119-67 


758079 







Cosine 


D. 


Sine 1 


1 

1 


Cotang. 


D. ' 


Tang. 


M. 



(89 DEGREES.) 



SINES AND TANGENTS. (1 DEGKEE.) 



19 



M. 


Siue 


D 




Cosine 


D. 


Tang. 


D 




Cotimj?. 


60 


o 


8.24185:5 


119 


63 


9.999934 


.04 


8.241921 


119 


.67 


11-758079 


I 


249033 


117 


68 


999932 


.04 


249102 


117 


•72 


ll 


2 


256094 


ii5 


80 


999929 


• 04 


256i65 


ii5 


•84 


3 


263o42 


ii3 


98 


999927 


• 04 


263ii5 


114 


.02 


736885 


57 


4 


269881 


112 


21 


999925 


• 04 


269956 


112 


•25 


73oo.i4 , 56 ! 


5 


276614 


no 


5o 


999922 


.04 


276691 


no 


•54 


723309 


55 


6 


283243 


108 


83 


999920 


•04 


283323 


108 


.87 


716677 


54 


7 


289773 


107 


21 


■ 9999 '8 


• 04 


289806 


107 


.26 


710144 


53 


8 


296207 


io5 


65 


999915 


• 04 


296292 


io5 


.70 


703708 


52 


9 


302546 


104 


i3 


999913 


.04 


3o2634 


104 


.18 


697366 


5i 


10 


308794 


102 


66 


999910 


.04 


308884 


102 


.70 


691116 


5o 


II 


8.314904 


lOI 


22 


9.999907 


.04 


8.3i5o46 


101 


.26 


11-684954 


% 


12 


321027 


l^ 


82 


999905 


.04 


32II22 


^ 


.87 


678878 


i3 


327016 


47 


999902 


• 04 


327114 


.5i 


672886 


47 


14 


332924 


97 


14 


999899 


c5 


333025 


97 


.19 


666975 


46 


i5 


338753 


9D 


86 


999897 


o5 


338856 


95 


90 


661144 


45 


i6 


344304 


94 


60 


999894 


o5 


344610 


94 


65 


655390 


44 


\l 


35oi8i 


93 


38 


999891 


o5 


3502S9 


93 


43 


6497 « I 


43 


355783 


92 


•i? 


999888 


o5 


35589D 


92 


24 


644 1 o5 


42 


19 


36i3i5 


% 


999885 


o5 


36i43o 


9' 


08 


638570 


41 


20 


366777 


90 


999882 


o5 


366895 


89 


95 


633 I o5 


40 


21 


8.372171 


88 


80 


9.999879 


o5 


8.372292 


88 


85 


11-627708 


It 


22 


377499 


87 


72 


999876 


o5 


377622 
382889 


87 


77 


622378 


23 


382762 


86 


67 


999873 


o5 


86 


72 


617111 


37 


24 


387962 


85 


64 


999870 


o5 


388092 
393234 


85 


70 


611908 


36 


25 


393101 


84 


64 


999%7 


o5 


84 


70 


606766 


35 


26 


398179 


83 


66 


999864 


o5 


398315 


83 


71 


601685 


34 


27 


4o3i99 


82 


71 


999861 


o5 


' 403338 


82 


It 


596662 


33 


28 


408161 


81 


77 


999858 


o5 


4o83o4 


81 


591696 


32 


29 


4i3o68 


80 


86 


999854 


o5 


4i32i3 


80 


91 


586787 


3i 


So 


4I79J9 


79 


96 


999851 


06 


418068 


80 


02 


581932 


3o 


3i 


8.422717 


?? 


09 

23 


9.999848 


06 


8.422869 


?^ 


14 


11.577131 


It 


32 


427462 


999844 


06 


427618 


3o 


572382 


33 


432156 


77 


40 


999841 


06 


43231 5 


77 


45 


567685 


27 


34 


436800 


76 


57 


999838 


06 


436962 


76 


63 


563o38 


26 


35 


441394 


75 


77 


999834 


06 


. 441360 


75 


83 


558440 


25 


36 


445941 


74 


99 


999831 


06 


446110 


75 


o5 


553890 


24 


37 


450440 


74 


22 


999827 


06 


45o6i3 


74 


28 


549387 


23 


38 


454893 


73 


46 


999823 


06 


455070 


73 


52 


544930 


22 


39 


439301 


72 


73 


999820 


06 


459481 
463849 


72 


79 


540019 


21 


40 


463665 


72 


00 


999816 


06 


72 


06 


536i5i 


20 


41 


8-467985 


71 


29 


9.999812 


06 


8.468172 


71 


35 


11.531828 


\l 


42 


472263 


70 


60 


999809 


06 


472454 


70 


66 


527546 


43 


47^498 


69 


91 


999805 


06 


476693 
480892 


69 


t 


523307 


17 


44 


480693 


tl 


24 


999801 


06 


tl 


519108 


16 


45 


484848 


59 


999797 


07 


485o5o 


65 


5 I 4950 
5io83o 


i5 


46 


488963 


67 


94 


999793 


07 


489170 
493250 


68 


01 


i4 


47 


493040 


67 


3x 


999790 
999786 


07 


67 


38 


506750 


i3 


48 


497078 


66 


69 


07 


497293 


66 


76 


502707 


12 


49 


5oio8o 


66 


08 


999782 


07 


501298 


66 


i5 


498702 


n 


5o 


5o5o45 


65 


48 


999778 


07 


505267 


65 


55 


494733 


10 


5i 


'VX 


64 


89 


9-999774 


07 


8.509200 


64 


t 


11-490800 
486902 


t 


52 


64 


3i 


999769 


07 


513098 


64 


53 


516726 


63 


75 


999765 


07 


516961 


63 


82 


483o39 


7 


54 


52o55i 


63 


19 


999761 


07 


520790 


63 


26 


479210 


6 


55 


524343 


62 


64 


999757 


07 


524586 


62 


72 


475414 


5 


56 


528102 


62 


II 


999753 " 


07 


528349 


62 


18 


47i65i 


4 


u 


531828 


61 


58 


999748 


07 


532080 


61 


65 


467920 


3 


535523 


61 


06 


999744 


07 


535779 


61 


i3 


464221 


2 


59 


539186 


60 


55 


999740 


07 


539447 


60 


62 


460553 


1 


60 


542819 


60-04 


99973d 


07 


543084 


60.12 


456916 







Cosine 


D. 


Sine 1 


Cotang. 


D. 


Tang 





16 



(88 DEGREES.) 



20 



(2 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sino 


D. 


Cosine 


D. 


Tang. 


D. 


Cotaug. 1 


o 


8.542HI9 


60-04 


9.999735 


-07 


8-548084 


60.12 


It .456916 i 60 


I 


546422 


59.55 


999781 


-07 


546691 


59 


•62 


453809 I 59 


2 


Itml 


59.06 
58.58 


999726 


.07 


550268 




•14 


449732 


58 


3 


999722 


.08 


558817 


58 


•66 


446188 


57 


4 


557054 


58.11 


999717 


-08 


557886 


58 


I'i 


442664 


56 


5 


56o54o 


57-65 


999718 


.08 


560828 


57 


439172 
433709 
482278 


55 


6 


563999 


57.19 


999708 


.08 


564291 


57 


27 


54 


I 


567431 


56.74 


999704 


-08 


567727 


56 


82 


53 


570836 


56-80 


999699 


-08 


571187 


56 


38 


428863 ! 52 i 


9 


574214 


55.87 


999689 


.08 


574520 


55 


t 


425480 


5i 


IC 


577566 


55.44 


.08 


577877 


55 


422128 


5o 


II 


8.580892 


55.02 


9.999685 


.08 


8-58i2o8 


55 


10 


11-418792 


it 


12 


584193 


54-60 


999680 


-08 


584314 


54 


68 


413486 


i3 


587469 


54-19 


999675 


-08 


587795 


54 


27 


4l2205 


47 


14 


590721 


53.79 


999670 


.08 


59.061 


53 


87 


408949 


46 


i5 


593948 


53.39 


999665 


.08 


594288 


53 


47 


405717 

4025(58 


45 


i6 


597T52 


58.00 


999660 


-08 


597492 


58 


08 


44 


\l 


6oo332 


52.61 


999655 


-08 


600677 


52 


70 


899828 


43 


603489 
606623 


52-23 


999650 


.08 


608889 
606978 


52 


32 


396161 


42 


»9 


51-86 


999645 


.09 


5i 


n 


898022 
3^9906 


41 


20 


609734 


5i 49 


999640 


.09 


610094 


5i 


40 


21 


8-612823 


51.12 


9.999635 


.09 


8-618189 


5i 


21 


1I-3868II 


39 


22 


610891 
6189^7 


50.76 


999629 


•Of; 


616262 


5o 


85 


388788 


3i 


23 


50-41 


999624 


-09 


619818 


5o 


5o 


880687 


37 


24 


621962 


5o-o6 


999619 


-09 


622843 


5o 


i5 


377657 


36 


25 


624965 


49-72 


999614 


-09 


625832 


49 


81 


374648 


35 


26 


627948 


49-38 


999608 


.09 


628840 


^ 


47 


371660 


34 


27 


630911 
633854 


49-04 
48-71 


999608 


-09 


681808 


a 


18 


368692 


33 


28 


999397 


-09 


634256 


80 


365744 
362816 


32 


29 


686776 


48.39 


& 


•09 


687184 


48 


48 


3i 


3o 


689680 


48.06 


.09 


640093 


48 


16 


359907 


3o 


3i 


8-642563 


47-75 


9.999581 


-09 


8-642982 


47 


84 


11-357018 


It 


32 


645428 


47-43 


999575 


-09 


643853 


47 


58 


354147 


33 


648274 


47-12 


999570 


-09 


648704 


47 


22 


351296 


27 


34 


65iio2 


46.82 


999564 


-09 


65i587 


46 


91 


348468 26 


35 


6589II 


46.52 


999558 


•10 


654352 


46 


61 


345648 25 


36 


656702 


46-22 


999553 


-10 


657149 


46 


3i 


342851 


24 


37 


659475 


45.92 


999547 . 


-10 


639928 


46 


02 


340072 


23 


38 


662280 


45.63 


999541 


•10 


662689 


45 


73 


887311 


22 


39 


664968 


45.35 


999535 


-10 


665438 


45 


44 


334567 


21 


40 


667689 


45-06 


999529 


-10 


668 160 


45 


26 


881840 


20 


41 


8.670893 
678080 


44-79 


9-999524 


-10 


8-670870 


44 


88 


11.829180 
826487 


]i 


42 


44-51 


999518 


-10 


673563 


44 


61 


43 


675751 


44-24 


999312 


-10 


676289 


44 


34 


828761 


17 


44 


678405 


43-97 


999506 


•10 


678900 


44 


17 


32II00 


16 


45 


681043 


43-70 


999500 


-10 


681344 


43 


80 


3 1 8456 


i5 


46 


683665 


43.44 


999408 
999487 


-10 


684172 


48 


54 


3i5828 


14 


tl 


686272 


43.18 


-10 


686784 


48 


28 


3i32i6 


i3 


688863 


42-92 


999481 


-10 


689881 


43 


08 


810619 


12 


49 


691488 


42-67 


999475 


•10 


691968 
694029 


42 


77 


808087 


II 


5d 


698998 


42.42 


999469 


•10 


42 


52 


3o547i 


:o 


5i 


8 696548 


42.17 


9.999463 


• II 


8-697081 


42 


28 


II. 802919 
3oo383 


t 


52 


699078 


41.92 


999456 


-11 


699617 


42 


o3 


53 


701589 


41.68 


999400 


• n 


702189 


41 


79 


297861 


1 


54 


.704090 


41-44 


999443 


-11 


704646 


41 


53 


295354 


6 


55 


706577 


41-21 


999487 


-II 


707140 


41 


82 


292860 


5 


56 


709049 


40-97 


999431 


-11 


709618 


41 


08 


290882 
28546? 


4 


u 


7a 1 507 
718952 
7^6383 


40.74 
40 -51 


999424 
999418 


-11 
-11 


712083 
714534 


40 
40. 


85 
62 


3 
2 


59 


40.29 


99941 1 


• II 


716072 
719396 


40. 


40 


288028 


I 


60 


718800 


40.06 


999404 


-11 


40-17 


280604 




M. 




Cosine 


J), 


Sme 




Cotang. 


D- 1 


Tang. 



(87 DEGREES.) 



SINES AND TANGENTS, (3 DEGKEES., 



21 



"m. 


fcjiiie 


D. 


Co.--iiie 


1>. 


Tang, 


D. 


Cotang. 


60 





8-7i88oo 


40.06 


9.999404 


.11 


8.719896 


40-17 


11.280604 


I 


721204 


39.84 


999398 


.11 


721806 


89-95 


278194 


It 


2 


723595 


39.62 


999391 


•11 


724204 


39-74 


275796 


3 


725972 
728337 
780688 


39.41 


999384 


• II 


726588 


89.53 


278412 


57 


4 


39-10 
38-98 


999378 


• II 


728959 
781817 


89-80 


271041 


56 


5 


909871 


•11 


89.09 


268683 


55 


6 


733027 


38-77 


999864 


.12 


788668 


88-89 


266887 


54 


I 


735354 


38-57 


999357 


•12 


785996 


38-68 


264004 


53 


737667 


38-36 


999350 


•12 


788817 


38-48 


261683 


52 


9 


739969 


38.16 


999343 


•12 


740626 


38-27 


259874 


5i 


10 


742259 


37-96 


999886 


•12 


742922 


38-07 


257078 


5o 


II 


8.744536 


mt 


9.999829 


• 12 


8.745207 


37-87 


11-254793 


^2 


12 


746802 


999822 


•12 


747479 


37-68 


252521 


48 


i3 


749055 


37-37 


999813 


.12 


■ 749740 


37-49 


25o26o 


47 


14 


751297 


37.17 


999808 


.12 


751989 


87-29 


24801 1 


46 


i5 


753528 


36.98 


999801 


.12 


754227 


87.10 


245773 


.45 


i6 


755747 


36.79 


999294 


.12 


756458 


86.92 


248547 


44 


\l 


757955 


36.61 


999286 


.12 


758668 


36.78 


241882 


43 


76oi5i 


36-42 


999279 


.12 


760872 


36-55 


289128 


42 


19 


762337 


36-24 


999272 


.12 


768065 


36.86 


286985 


41 


20 


7645 1 1 


36 -06 


999265 


.12 


765246 


36.18 


284754 


40 


21 


8.766675 


35.88 


9.999257 


•12 


8.767417 


36-00 


11-282583 


39 


22 


768828 


35.70 


999250 


.13 


769578 


35-88 


280422 


88 


23 


770970 


35.53 


999242 


•l3 


771727 


35-65 


228278 


ll 


24 


773101 


35.35 


999283 


.13 


778866 


35-48 


226184 


25 


773223 


35.18 


999227 


.13 


775995 


35-3i 


224005 


85 


26 


777333 


35-01 


999220 


•i3 


778114 


35-14 


221886 


84 


11 


7^9434 


34-84 


999212 


•i3 


780222 


34-97 


219778 


38 


•78i524 


34-67 


999205 


• i3 


782820 


34-80 


217680 


32 


29 


7836o5 


34-51 


999197 


.18 


784408 


34-64 


215592 


3i 


3o 


785675 


34-31 


999189 


•i3 


786486 


34-47 


2i85i4 


3o 


3i 


8.787736 


34-18 


9.999181 


• i3 


8.788554 


34-3i 


11-211446 


29 


32 


789787 


34-02 


999 '74 


• 18 


790613 


34- 15 


209887 


28 


33 


791828 


33-86 


999166 


.i3 


792662 


38-99 


207888 


27 


34 


793859 


33-70 


999158 


.13 


794701 


33-83 


205299 


26 


35 


795881 


33-54 


9991 5o 


.i3 


796781 


33-68 


208269 
201248 


25 


36 


797894 


33-39 


999142 


.18 


798752 


33-52 


24 


ll 


799897 


33-23 


999134 


.18 


800768 


33-37 


199287 
197285 


23 


001892 


33-08 


999126 


.i3 


802765 


33-22 


22 


39 


803876 


32.93 


099118 


• 13 


804758 


33-07 


195242 


21 


40 


8o5852 


32.78 


9991 10 


• 13 


806742 


32-92 


198258 


20 


41 


8.807819 


32-63 


9.999102 


• i3 


8.808717 


32-78 


11.191283 
189817 


\l 


42 


809777 


32-49 


999094 


•14 


810688 


82-62 


43 


811726 


32.34 


999086 


-14 


81 2641 


32-48 


187859 


17 


H 


8i366t 


32.19 
32.05 


999077 


•14 


814589 


32-33 


185411 


16 


45 


815599 


999069 


•14 


816529 


82-19 
32-o5 


183471 


i5 


46 


•817522 


31.91 


999061 


•14 


8 1 8461 


181589 


14 


tl 


819436 


31-77 


999053 


-14 


820884 


81-91 


179616 


i3 


821343 


3i.63 


999044 


•14 


822298 


31-77 


177702 


12 


49 


823240 


3 1. '49 


999086 


•14 


824205 


31-63 


175795 


11 


5o 


825i3o 


31.35 


999027 


•14 


826108 


3i-5o 


178897 


10 


5. 


8.827011 


3l.22 


9.999Q19 


•14 


8-827992 
829874 


31-36 


11.172008 


I 


5j 


828884 


3i.o8 


999010 


•14 


31-23 


170126 


53 


830749 


3o.o5 
30.82 




•14 


881748 


3i.io 


168252 


7 


54 


832607 


•14 


8386i3 


30-96 
3o-83 


166887 


6 


55 


834456 


3o.6g 


•14 


885471 


164529 


5 


56 


836297 


30.56 


998976 


•14 


887821 


30-70 


162679 


4 


u 


838i3o 


30.43 


998967 
998958 


.i5 


889168 


80-57 


160887 


3 


839956 


3o.3o 


.i5 


840998 


30-45 


159002 


2 


59 


liuii 


3ovi7 


998950 


• 15 


842825 


30-32 


157175 


I 


6o 


3o.oo 


998941 


.15 


844644 


80-19 


155356 





Cosine 


D. : 


Sine 




Cotang. i 


D. 


Tang. 


IVL 



(86 DEGREES.) 



(4 DEGREES.:* A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


CJoeine 


D. 


Tang. 


D. 


Cotang. 


P 





8-843585 


3o.o5 


9.998941 


• 15 


8-844644 


30-19 


11-155356 


I 


845 3S7 


29-92 


99H932 


•ID 


846455 


30-07 


153545 


u 


3 


847183 


2980 


99^923 


• 15 


848260 


29.05 
29.82 


i5i74o 


3 


84S971 


29-67 


9989,4 


•i5 


85oo57 


',imi ! 5 


4 


85o75i 


29-55 


998905 


.i5 


85 I 846 


29.70 


5 


852525 


29-43 


998806 
998887 


• 15 


853628 


29.58 


146372 ! 55 


6 


854291 


29-3l 


.15 


8554^3 


29-46 


144597 1 54 


7 


856049 


29-19 


99SS78 


.15 


857171 


29-35 


142829 ! 53 
141068 52 


8 


857801 


TJ, 


998S69 


•15 


858932 


29-23 


9 


859546 


998S60 


•15 


8606S6 


29.11 


139314 


5i 


IC 


861283 


28.84 


998851 


•i5 


862433 


29-00 


137567 


5o 


II 


(j-863oi4 


28-73 


9-99MS41 


.15 


8.864173 


28-88 


11.135827 


t 


12 


864733 


28-61 


998832 


.i5 


865906 


28 -t7 


134094 


i3 


866455 


28.50 


998823 


.16 


867632 


28-66 


132368 


47 


14 


868 165 


28.39 


99S813 


.16 


869351 


28.54 


130649 


46 


i5 


869*^68 


28-28 


99S804 


.16 


871064 


28.43 


128936 


45 


i6 


871565 


28 17 


99S795 


16 


872770 


28-32 


12-230 


44 


17 


873255 


28-06 


99^785 


16 


874469 


1 28-21 


12^531 


43 


18 


8749^8 


27-95 


908776 


.16 


876162 


28-11 


123838 


42 


19 


876615 


27.86 


998766 


.16 


877849 


28-00 


12?l5l 


41 


20 


878285 


27-73 


998757 


• 16 


879529 


27.89 


1:0471 


40 


21 


8-819949 


27^63 


9-998747 


.16 


8-881202 


27- 79 


11.118^98 


39 


22 


as 1607 


27.52 


998738 


.16 


8«2869 


27-68 


117l3l 


38 


23 


883258 


27.42 


99«728 


.16 


884530 


27-58 


1 1 5470 


37 


24 


884903 


27-31 


99^718 


.16 


886i85 


27-47 


ii3Si5 


36 


25 


886542 


27-21 


99S-708 


.16 


887833 


07.37 


112167 


35 


26 


8S8174 


27-11 


99S699 


.16 


-889476 


27-27 


II0524 


34 


27 


8S9801 


27-00 


9986H9 


.16 


891112 


27-17 


108888 


33 


28 


891 42 1 


26-90 


99S679 


.16 


892742 


27.07 


10^258 32 1 


29 


893035 


26 -So 


99^^669 


-n 


894366 


26-97 


105634 


3i 


So 


894643 


26-70 


998659 


•n 


895984 


26-87 


104016 


3o 


3i 


8-896246 


26-60 


9 -99^649 


•17 


8.897596 


26.77 


11-102404 


S 


32 


807843 


26-51 


998639 


•17 


899203 


26-67 


100797 


33 


899432 


26.41 


998629 


•n 


900803 


26-58 


099197 


27 


34 


901017 


26.31 


99% 1 9 


•n 


902398 


26-48 


09-602 


26 


35 


902596 


26-22 


998609 


•17 


903987 


26-38 


096013 


25 


36 


904169 


26-12 


998599 


•17 


905570 


26-29 


094430 


24 


ll 


905736 


26-03 


998589 


•»7 


907147 


26-20 


092853 


23 


907297 


25-93 


998578 


•n 


908719 


26-10 


091 281 


22 


39 


908853 


25-84 


998568 


•n 


910285 


26-01 


oS?i54 


21 


40 


910404 


25-75 


998558 


•17 


911846 


25-92 


20 


41 


'V^U 


25-66 


9-998548 


•17 


8.913401 


25-83 


i,.d86599 


'R 


42 


25-56 


998537 


•'7 


914951 


25--4 


o'Jno4Q 


18 


43 


9l5o2-2 


25-47 


91^8527 


•17 


916495 
918034 


25-65 


o^^'f'^o^ 


'7 


44 


9i655o 


25-38 


998516 


•i8 


25-56 


o8f96'> 


16 


45 


91S073 


25-29 


998506 


•18 


919568 


25-47 


080432 ! 


i5 


46 


9 1 9591 


25-20 


99^495 


•18 


921096 


25-38 


0-8904 ; 


:4 


47 


921.03 


25-12 


99«485 


•18 


922619 


25 -3o 


°'ll^' 


i3 


48 


922610 


25 -o3 


99«474 


•18 


924136 


:5-2i 


073864 


la 


49 


934112 


24-94 


99«464 


.18 


925649 


25-12 


074351 ! 


II 


5o 


935609 


24-86 


99«453 


•18 


927156 


25-o3 


072844 j 


10 


5i 


8 92-rioo 


24-77 


9 •99-3442 


.»8 


8-928658 


24-95 
24-86 


II 07134: j 


t 


1 52 


928587 


24-69 


998431 


.18 


9301 55 


069845 
068353 


53 


930068 


24-60 


99*^431 


.18 


931647 


24-78 


1 


54 


93 1 544 


24-52 


998410 


.18 


933,34 


24-70 


066866 


5 


55 


93301 5 


24-43 


99S399 


.18 


934616 


24-6> 


0653.84 


5 


56 


934481 


24.35 


998388 


.]8 


o36oq3 


24-53 


o63qo7 


4 


u 


935942 


24-27 


998377 


.18 


937565 


24-45 


062435 


3 


937398 


24-19 


998366 


.18 


939032 


24-37 


060968 


a 


59 


9^8850 


24-11 


99<^355 


.18 


940404 


24 -30 


o5o5o6 


1 


60 


940296 


24 -o3 


99^^344 


■18 


9419^2 


24-21 


008048 [ 


I 

I 


Cosine 


D. 


Sine i 


1 


Cotang 


D. 


Tang. 1 M. 



(85 DEGREES.) 



SINES AND TANGENTS. (5 DEGREE.) 



23 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotiuig. 





8-040296 


24 -03 


9.998344 


.19 


8.941952 


24-21 


1 1 -058048 


60 


I 


941738 


23 


:l^ 


998333 


.19 


948404 


24.13 


056596 


u 


2 


943174 


28 


998822 


•19 


944852 


24.05 


o55i48 


3 


944606 


23 


•79 


998811 


.19 


946295 
947734 


23-97 


o537o5 


u 


4 


94.6084 


23 


•71 


998800 


.19 


23.90 


052266 


5 


947456 


23 


.63 


998289 


.19 


949168 


23-82 


o5o832 


55 


6 


948874 


23 


.55 


998277 


.19 


950597 


28.74 


349408 54 


7 


930287 


28 


■48 


998266 


.19 


952021 


23.66 


047979 ! 53 


8 


951696 


28 


•40 


998255 


.19 


953441 


28-60 


046559 


52 


9 


953100 


23 


.32 


998243 


.19 


954856 


28.51 


045144 


5i 


10 


954499 


23 


•25 


998282 


.19 


956267 


23.44 


048788 


5o 


12 


8. 955^94 

957284 


23 

23 


•17 

.lO 


9.998220 
998209 


•19 
.19 


8.957674 
959075 


23-37 
28.29 


11-042826 
040925 


8 


i3 


938670 


23 


.02 


998197 


.19 


960473 


28-23 


089527 


47 


U 


960052 


22 


.tl 


998186 


.19 


961866 


28-14 


088184 


46 


1 5 


961429 


22 


998174 


.19 


968255 


23.07 


036745 


45 


i6 


962801 


22 


.80 


998163 


.19 


964689 


23.00 


o858bi 


44 


\l 


964170 


22 


.73 


998151 


.19 


966019 


22.93 
22.86 


088981 


43 


965534 


22 


• 66 


998.89 
998128 


•20 


967394 
968766 


082606 


42 


^9 


966893 


22 


.59 


•20 


22-79 


081284 


41 


20 


968249 


22 


.52 


998116 


•20 


970133 


22.71 


029867 


40 


2l 


8.969600 


22 


•44 


9.908104 


•20 


8-971496 


22-65 


11-028504 


ll 


22 


970947 


22 


38 


998092 
998080 


•20 


972835 


22.57 


027145 


23 


972289 


22 


3i 


•20 


974209 


22.51 


025791 


37 


24 


978628 


22 


24 


998068 


•20 


975560 


22.44 


024440 


36 


25 


974q62 


22 


•7 


998056 


•20 


976906 


22.87 


028094 


35 


26 


976293 


22 


10 


998044 


•20 


978248 


22.30 


021752 


34 


11 


977619 


22 


o3 


998082 


•20 


979586 


22-23 


020414 


33 


978941 


21 


97 


998020 


•20 


980921 


22-17 


019079 


32 


?9 


980259 
981573 


21 


r. 


998008 


•20 


982251 


22-10 


01^749 


3i 


So 


21 


997996 


•20 


988577 


22-04 


016428 


3o 


3i 


8.982883 


21 


11 


9.997985 


•20 


8-984899 


21-97 


ii.oi5ioi 


29 
28 


32 


984189 


21 


70 


997972 


•20 


986217 


21-91 


018788 


33 


985491 


21 


63 


997959 


•20 


987582 


21-84 


012468 


27 


34 


^a 


21 


57 


997947 


•20 


988842 


21.78 


oiii58 


26 


35 


21 


5o 


997935 


•21 


990149 


21.71 


ooq85i 
008549 


25 


36 


989374 


21 


44 


997922 


•21 


99:451 


21.65 


24 


57 


990660 


21 


88 


997910 


•21 


992750 


2t-58 


007250 


23 


38 


991943 


2i 


81 


997897 


•21 


994045 


21-52 


005955 


22 


39 


998222 


21 


25 


997885 


•21 


995887 


21-46 


004663 


21 


4o 


994497 


21 


^9 


997872 


•21 


996624 


21.40 


008876 


20 


4i 


8.995768 


21 


12 


9.997860 


•21 


8.997908 


21-34 


11-002092 


\t 


42 


997086 
998299 


21 


06 


997847 


•21 


999188 


21-27 


000812 


43 


21 


00 


997885 


•21 


9-000465 


21-21 


10-999535 


\l 


44 


999D60 


20 


94 


997822 


•21 


001788 


21-15 


99H262 


45 


9.000816 


20 


87 


997809 


•21 


008007 


21-09 


996998 


i5 


:i6 


002069 
008818 


20 


82 


997797 


•21 


004272 


21-03 


995728 


14 


47 


20 


76 


997784 


•21 


005534 


20-97 


994466 


i3 


48 


004568 


20 


70 


997771 


•21 


OU6792 


20-91 


998208 


12 


49 


oo58o5 


20 


64 


997758 


.21 


008047 
009298 


20-85 


991953 


II 


53 


007044 


20 


58 


997745 


.21 


20-80 


990702 


13 


5i 


9.008278 


20 


52 


9.997782 


.21 


J9. 01 0546 


20-74 


10-989454 


I 


52 


oog5io 


20 


46 


997719 


•21 


011790 
018081 


20-68 


988210 


53 


010787 


20 


40 


997706 


•21 


20-62 


986969 


I 


54 


011962 


20 


34 


997698 


•22 


014268 


20-56 


985782 


55 


018182 


20 


29 


997680 


•22 


oi55o2 


20- 5l 


984498 


5 


56 


014400 


20 


28 


997667 


•22 


016782 


20-45 


988268 


4 


ll 


0i56i3 


20 


17 


997654 


•22 


017919 


20-40 


982041 


3 


016824 


20 


12 


997641 


.22 


019188 


20-88 


980817 


2 


^ 


018081 


20 


06 


997628 


.22 


020408 


20-28 


979597 
97§38o 


: 


60 


019235 


20-00 


997614 


.22 


021620 


20-28 







Cotiue 


D. 


Sine 




Cotanc^. 


P. 


_J'l'^'^ _ 


~£\ 



(84 DEGREES.) 



24 



v6 DEGREES.) A TABLE OF LOGARITHMIC 



M 




Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




9-019235 


20-00 


9-997614 


-22 


9-021620 


20-23 


10-978380 


60 


I 


020435 


19 


% 


997601 


•22 


022834 


20 


•17 


977166 ' 59 1 


3 


02I632 


19 


997588 


•22 


024044 


20 


11 


975956 


58 


3 
4 


022825 
024016 


19 
19 


84 
78 


997574 
997561 


-22 

•22 


02525l 

026455 


20 
20 


06 
00 


974749 
973545 


U 


5 


025203 


19 


73 


997547 


•22 


027655 


19 


95 


972345 55 


6 


026386 


19 


67 


997534 


•23 


028852 


19 


90 


971148 54 


I 


027367 


19 


62 


997520 


•23 


o3oo46 


19 


85 


969954 53 
968763 52 


028744 


19 


57 


997507 


•23 


o3i237 


19 


79 


9 


029918 


19 


5i 


9974q3 
997480 


•23 


o32425 


19 


74 


967575 


5i 


ic 


031089 


19 


47 


•23 


o336o9 


19 


69 


966391 


5o 


II 


9-o32257 


19 


41 


9-997466 


•23 


9-034791 


19 


64 


10-965209 


% 


12 


o3342i 


19 


36 


997452 


•23 


035969 


19 


58 


964031 


i3 


034582 


19 


3o 


997439 
997425 


•23 


037144 


19 


53 


962856 


47 


14 


035741 


19 


25 


•23 


o383i6 


19 


48 


961684 


46 


I') 


C36896 


19 


20 


99741 1 


•23 


039485 


19 


43 


96051 5 


45 


lb 


o38o48 


'9 


i5 


997397 


•23 


04065 1 


19 


38 


95g349 


44 


I? 


039197 


19 


10 


997383 


•23 


041813 


19 


33 


938187 


43 


i8 


040342 


It 


o5 


997369 


•23 


042973 


19 


28 


937027 


42 


19 


04 1 485 


99 


997355 


•23 


044 i3o 


19 


23 


933870 


41 


20 


042625 


18 


94 


997341 


• 23 


045284 


19 


18 


954716 


40 


21 


9.043762 


18 


89 


9-997327 


•24 


9-046434 


10 


i3 


10-953566 


ll 


22 


044895 


18 


84 


99731 3 


•24 


047582 


'9 


08 


932418 


23 


046026 


18 


79 


697209 


•24 


048727 


19 


o3 


95,273 


37 


24 


047154 


18 


73 


997283 


•24 


049869 
o5ioo8 


18 


98 


9501 3i 


36 


25 


048279 


18 


70 


997271 


•24 


18 


t 


948992 


35 


26 


049400 


18 


65 


997257 


•24 


o52i44 


i8 


947836 


34 


^J 


o5o5i9 


18 


60 


997242 


•24 


053277 


18 


84 


946723 


33 


o5i63d 


18 


55 


997228 


•24 


054407 


18 


79 


9455c}3 


33 


29 


052749 


18 


5o 


997214 


•24 


055535 


18 


74 


944465 


3i 


So 


. 053859 


18 


45 


997199 


•24 


056659 


18 


70 


943341 


3o 


3i 


9-054966 


18 


41 


9-997185 


•24 


9-057781 


18 


65 


10-942219 


\l 


32 


056071 


18 


36 


997170 


•24 


058900 


18 


S 


94U00 


33 


lU^', 


18 


3i 


997156 


• 24 


060016 


18 


9399«4 


27 


34 


18 


27 


997141 


•24 


061 i3o 


18 


5i 


938870 


26 


35 


059367 


18 


22 


997127 


•24 


062240 


18 


46 


937760 


25 


36 


060460 


18 


17 


997112 


•24 


063348 


18 


42 


936652 


24 


37 


o6i55i 


18 


i3 


997098 


•24 


064453 


18 


37 


935547 


23 


38 


062639 


18 


08 


997083 


•25 


065556 


18 


3? 


934444 


22 


39 


063724 


18 


04 


997068 


•25 


066655 


18 


28 


933345 


21 


40 


064806 


n 


99 


997033 


•25 


067752 


18 


24 


932248 


20 


41 


9-065885 


17 


94 


9-997039 


•25 


9-068846 


18 


19 


10-931 i54 


\l 


42 


066962 


17 


90 


997024 


•25 


069938 


18 


i5 


930062 


43 


o68o36 


17 


86 


997009 


•25 


071027 


18 


10 


928973 


17 


44 


069107 


17 


81 


996994 


-25 


0721 13 


18 


06 


927H87 


16 


45 


070176 


n 


77 


996979 


•25 


073197 


18 


02 


926803 


i5 


46 


071242 


17 


72 


996964 


•25 


°7427S 


17 


97 


923722 


14 


47 


072306 


17 


68 


996949 


•25 


073336 


17 


93 


924644 


i3 


48 


073366 


n- 


63 


996934 


•25 


076432 


17 


^9 


923568 


12 


49 


074424 


17- 


59 


996919 


•25 


0775o5 


n 


84 


922495 


II 


5o 


075480 


17 


55 


996904 


•25 


078576 


n 


80 


921424 


13 


5i 


9.076533 


17 


5o 


9.996889 


• 25 


9-079644 


17 


76 


io-92o356 


I 


5a 


077583 


17 


46 


996874 


•25 


0807 1 


'-7 


72 


919290 


53 


078631 


17 


42 


996858 


•25 


081773 


17 


67 


918227 


I 


54 


079676 


17 


38 


996843 


•25 


0S2833 


17 


63 


917167 


55 


080719 


17 


33 


996828 


•25 


083891 


17 


59 


916109 


5 


56 


081759 


17 


29 


996812 


• 26 


084947 


n 


53 


9i5o33 


4 


57 


082797 
083832 


17 


25 


996707 


.26 


086000 


17 


5i 


914000 


3 


58 


17 


21 


996782 


.26 


087050 
088098 


17 


% 


912950 


a 


59 


084864 


17 


»7 


996766 


.26 


17 


91 1902 
910856 


I 


66 




085894 


17 i3 


996751 


.26 


089144 


17 38 





Cosine 


1). 


Sine. 




Cotansr. 


D. 


Tang. 


xM. 



(83 DEGREES.) 



SINES AND TANGENTS. (7 DEGREES.) 



2c 



M. 


Sine 


D. 


Cosine 


D. 


1 Tang. 


1 ^' 


Cotaiig. 1 


o 


9.085894 


17-13 


9-996751 


.26 


9-089.44 


17-38 


io-9io856 60 


1 


086922 


17.09 


996735 


.26 


09018/ 


17-34 


909813 So 
908772 [ 5§ 


a 


087947 
088970 


17-04 


996720 


.26 


09122S 


i7-3o 


i 


17.00 


996704 


•26 


092266 


17-27 


TXs u 


4 


089990 


16.96 


996688 


.26 


093302 


17-22 


5 


091008 


16.92 
16-88 


996673 


.26 


094336 


17.19 
17-15 


905664 ; 55 


6 


092024 


996657 


.26 


095367 


904633 i 54 


7 


093037 


16.84 


996641 


.26 


OCJ6395 


17-11 


9o36o5 ': 53 


8 


094047 


16.80 


996625 


.26 


1 097422 


17-07 


905578 52 


Q 


090036 


16.76 


996610 


.26 


098446 


17-03 


901354 i 5i 


10 


096062 


16.73^ 


996094 


.26 


099468 


16.99 


900032 Do 


II 


9-097065 


16. 6S" 


9-996578 


.27 


9-100487 


16.95 


10-899313 49 

89849^) 1 48 
897481 ! 47 


12 


098066 


16.65 


996062 


•27 


ioi5o4 


16.91 


i3 


099065 


16.61 


996346 


•27 


I023I9 


16.87 


14 


100062 


16.57 


996530 


•27 


103532 


16.84 


896468 i 46 


i5 


ioio56 


16.53 


996514 


•27 


104542 


16-80 


895458 i 45 


i6 


102048 


16-49 


996498 


•27 


io555o 


16-76 


894450 1 44 


17 


io3o37 


16-40 


996482 


•27 


106556 


16.72 


893444 ; 43 


i8 


io4o25 


16.41 


996465 


•27 


107559 


16.69 


892441 42 


19 


io5oio 


16.38 


996449 


•27 


io856o 


16.63 


• 891440 1 41 


20 


105992 


16-34 


996433 


•27 


109559 


16.61 


890441 1 40 


21 


9.106973 


i6-3o 


9-996417 


•27 


9-110556 


16-58 


10-889444 ' 39 
888449 38 


22 


107931 


16-27 


996400 


• 27 


11135l 


16-54 


23 


108927 


16-23 


996384 


•27 


112343 


16. 5o 


887457 37 


24 


I 0990 I 
1 10873 


16.19 


996368 


•27 


113533 


16-46 


8S6467 36 


25 


16-16 


996331 


•27 


114521 


16-43 


883479 35 


26 


111842 


16-12 


996335 


•27 


115307 


16-39 


884493 , 34 


27 


1 1 2809 


16-08 


996318 


•27 


116491 


i6-36 


883309 
882528 


33 


28 


113774 


16. o5 


9g63o2 


.28 


117472 


16-32 


32 


29 


1 14737 


i6-oi 


996285 


.28 


118432 


16-29 
16-25 


881548 


3i 


3o 


115698 


i5-97 


996269 


.28 


119429 


880571 


3o 


3i 


9.116656 


15-94 


9-996232 


.28 


9-120404 


16-22 


'"■1%^ \ It 


32 


m6i3 


15-90 
15-87 


996235 


.28 


121377 


16.18 


33 


1 1 8567 


996219 


.28 


122348 


16. i5 


l%ll i U 


34 


119319 


15-83 


996202 


.28 


125317 


16-11 


35 


1 20469 


i5.8o 


996185 


.28 


124284 


16-07 


875716 25 


36 


121417 


15.76 


996168 


.28 


123249 


16-04 


874751 . 24 


37 


122362 


15.73 


9961 5i 


.28 


1 262 II 


16-01 


873789 23 

872828 23 


38 


i233o6 


15.69 


996134 


.28 


I27172 


15-97 


39 


124248 


i5.66 


996117 


.28 


i28i3o 


15-94 


871870 21 


40 


120187 


15-62 


996100 


.28 


129087 


15-91 


870913 20 


41 


g.126125 


\l-M 


9-996083 


• 29 


9'i3oo4i 


15-87 


10-869939 19 


42 


127060 


996066 


•29 


1 30994 


15-84 


43 


127993 


i5.52 


996049 


.29 


i3i944 
132893 


i5.8i 


86^056 I7 
867107 16 


,44 


128925 
129834 


15.49 
15.45 


996032 


.29 


15.77. 


45 


9960 1 5 


.29 


133839 


15-74 


866161 


46 


130781 


15.42 


993998 


•29 


1347H4 


15.71 


860216 14 


47 


i3i7o6 


15.39 


995980 


•29 


135726 


15-67 


864274 1 3 


48 


1 32630 


15.33 


993963 


• 29 


136667 


i5-64 


863333 


12 


49 


133551 


i5.32 


995946 


• 29 


i376o5 


i5-6i 


862395 


II 


50 


134470 


15.29 


995928 


.29 


138542 


15-58 


861438 


10 


5i 


9.135387 
i363o3 


15.25 


9.995911 
993894 


.29 


9-139476 


15-55 


io-86o524 


I 


52 


l5-22 


•29 


140409 


i5-5i 


839591 
858660 


53 


137216 


15-19 


995876 


•29 


141340 


15-48 


I 


54 


138128 


i5.i6 


995839 


•29 


142269 


i5-45 


857731 


55 


139037 


I5.I2 


995841 


•29 


143196 


i5-42 


856S04 


5 


56 


139044 
140830 


15.09 


995823 


.29 


144121 


15-39 


830879 i 


4 


II 


i5-o6 


993806 


•29 


145044 


15-35 


854956 1 


3 


141754 


i5-o3 


993788 


•29 


1 43966 


15-32 


854034 ' 


2 


59 


142655 1 


15-00 


995771 


•29 


146885 


15-29 


853.15 ; 


» 


60 


143555 1 


14-96 i 


995753 1 


•29 


147803 


15-26 


852197 ! 





Cosine < 


D. 


Sine ' 




Cotiinor. 


D. 1 


Tims. 



(82 DEGKEE8.) 



26 


(8 


DEGREES.) A ' 


FABLE OF LOGAKJIH 


MIC 

ii.'mg. 




~M. 


j Sine 


: D- 


Cosine 


D. 


Tang. 


D. 


i 


o 


j 9-143555 


■ 14-96 


9-995753 


•30 


9-i47?o3 


15-26 


:o 852197 


60 


I 


I444J3 


14-93 


995735 


-30 


1 148718 


13.23 


85.2^2 


U 


2 


! 145340 


14-90 


993717 


-30 


! 149632 


15-20 


850 368 


3 


, 146^43 


14-87 


995099 


•30 


i i5o544 


15..7 


8494^6 


57 


4 


1471 36 


14-84 


993681 


•3o 


i5i454 


15-14 


84N346 


56 


5 


' 14^026 


14-81 


993664 


•3o 


152363 


i5-ii 


84-637 


55 


6 


i48oi5 


: 14-78 


9Q5646 


•3o 


153269 


i5-o8 


846-^31 


54 ' 


7 


.49302 


■ 14-75 


1 995628 


.30 


154174 


i5.o5 


843«26 


53 


i 


' 1D0686 


14-72 


j 993610 


•3o 


i55o77 


l5-02 


844923 


5a 


9 


i5i569 


1469 


1 995591 


•3o 


155978 


14-99 


84402? 


31 


10 


i5245i 


1 14-66 


! 995573 


•3o 


156877 


14-96 


843 1 i3 


30 


15 


9-1 J33o 


j 14-63 


1 9-995555 


• 30 


9- 157775 


14-93 


10-842225 


8: 


12 


1 54208 


1 14-60 


1 993337 


•30 


158671 


\iX 


841329 


i3 


i55o«3 


14-57 


1 993319 


•3o 


I 5g565 


840435 


47 


U 


155957 
i56B3o 


14-54 


993301 


• 3i 


160457 


14-84 


839343 
83%33 


46 


ID 


14-51 


9954«2 


-31 


16 1 347 


14-81 


45 


16 


137700 


14-48 


995464 


-31 


162236 


14-79 


83-7-64 


44 


»7 


158569 


14-45 


993446 


.3i 


i63i23 


14-76 


8368-'7 


43 


i8 


159435 


14-42 


993427 


•31 


164008 


14-73 


83^992 


42 


»9 


i6o3oi 


14-39 


093409 


•3i 


164^92 


14-70 


83 3 108 


41 


20 


161164 


14-36 


' 995390 


-3i 


165774 


14-67 


834226 


40 


21 


9-162025 


14-33 


9-9933-2 


.3i 


9-166654 


14-64 


10-833346 


It 


22 


162885 


i4-3o 


995353 


.31 


167532 


14-61 


832468 


23 


163743 


14-27 


993334 


.3i 


168409 


14-58 


83(391 


37 


24 


164600 


14-24 


993316 


-31 


1692S4 


14-55 


83o^)6 


36 


25 


165454 


14-22 


993297 


-3i 


170157 


14-53 


829843 


35 


26 


i663o7 


14-19 


99^278 


-31 


171029 


14- 5o 


82 V I 


34 


27 


167,59 
168008 


14-16 


995260 


.31 


I7i«99 


14-47 


82«I0I 


33 


28 


U-i3 


99^241 


.32 


172-67 


14-44 


82-233 


32 


29 


168856 


14-10 


993222 


.32 


173634 


14-42 


826366 


3i 


3o 


169702 


14-07 


993203 


.32 


174499 


14-39 


825501 


3o 


3i 


9- 170547 


i4-o5 


9-995i«4 


•32 


9-175362 


14-36 


10-824638 


It 


3c 


17.3R9 


14-02 


993165 


•32 


176224 


14-33 


8237-6 


33 


172230 


13-99 


995146 


•32 


1770^4 


14-31 


822916 


27 


34 


1730-0 


13-96 


993127 


.32 


177942 


14-28 


82305s 


26 


35 


173908 


13-94 


993108 


.32 


178799 


14-23 


821201 


25 


36 


174744 


13-91 
13-88 


9950^^9 


.32 


I7y655 


.4-23 


820345 


24 


37 


175578 


990070 


.32 


i8o5o8 


14-20 


819492 


23 


38 


■ 176411 


13-86 


995o5i 


.32 


i8i36o 


14-17 


81^^640 


22 


39 


. 177242 


i?-83 


Q95o32 


•32 


182211 


14-15 


8.7-^9 


21 


4o 


178072 


i3-8o 


995oi3 


.32 


i83o59 


14-12 


8i6q4l 


20 


41 


9-178900 


13-77 


9 994993 


.32 


9-183907 


14-09 


10-816093 


',1 


42 


179726 


13-74 


994974 


.32 


184752 


14-07 


813248 


43 


i8o55i 


13-72 


994935 


.32 


185597 


14-04 


814403 


}-l 


44 


181374 


13-69 


994935 


.32 


186439 


14-02 


813^61 


16 


45 


182196 


13-66 


994916 


.33 


1872S0 


.3-99 


812-20 


i5 


46 


i83oi6 


13-64 


994V 


.33 


188120 


.3-96 


8n«8o 


14 


47 


183834 


i3-6i 


994''^77 


.33 


188908 


.3-93 


811042 


.3 


48 


18465 I 


i3-5> 


994857 


• 33 


189794 


.3-91 


810206 


13 


49 


185466 


i3-5b 


994H38 


.^3 


190629 


13-89 


8093-1 


II 


5o 


186280 


13-53 


994^18 


.33 


191462 


.3-86 


808533 


10 


5i 


9-187092 


i3-5i 


9-994-98 


.33 


9-192294 


.3-84 


io-8o--o6 


I 


52 


187903 


13-48 


9947-9 


.33 


193124 


.3-8. 


806^76 


53 


188712 


13-46 


994^39 


.33 


193953 


13-79 


806047 


I 


54 


189519 


13-43 


994-39 1 


.33 


1947^0 


.3.76 


8o5220 


55 


190325 


13-41 


994-19 


.33 


195606 


i3-74 


804394 


5 


56 


191 i3c 


i3-33 


994-00 


.33 


196430 


13-71 


8o357o 




57 


191933 


13-36 


994680 


.33 


io-'253 


.3-69 


802747 




58 


192734 


13-33 


994660 


•33 


198074 


i3-66 


801926 




59 


193534 


i3.3o 


994640 


•33 


198894 


13-64 


801106 




6o 


194332 


13-28 


994620 


• 33 


199713 


i3-6i 


800287 


.¥f. 




Cosine I 


D. 


Sii.e 


i 


Cotanir. 


D. i 


Tui.'?. 








(81 I 


3EGR] 


EES.) 









SINES AND TAXGEXTS. (9 DEGREE.) 



27 



M.' 




Sine 


D. 


Co3ine 


D. 


Tang, 


D. 


Cotang. 




9-194332 


13.28 


9-994620 


.33 


9.199713 


i3-6i 


10-800287 60 1 


I 


193129 


i3 


26 


994600 


.33 


200329 


i3 


59 


799471 ' 59 


2 


193923 


i3 


23 


994580 


.33 


201343 


i3 


56 


798655 58 


3 


196719 


i3 


21 


994360 


34 


202159 


:3 


34 


797841 57 
797029 56 


4 


197311 


i3 


18 


^94540 


•34 


202971 


i3 


52 


5 


19S302 


i3 


16 


994319 


•34 


203782 


i3 


49 


796218 , 55 


6 


199091 


i3 


i3 


994499 


•34 


204392 


i3 


47 


795408 1 54 


7 


199S79 


i3 


1 1 


994479 


•34 


2o54oo 


i3 


43 


794600 53 


8 


200666 


i3 


08 


994439 


•34 


206207 


i3 


42 


793-93 ; 5.2 


9 


20 1 43 1 


1 3 


06 


994438 


•34 


207013 


i3 


40 


792987 i 5i- 


10 


202234 


i3 


04 


994418 


•34 


207817 


i3 


38 


792x83 5o 


II 


9 2g3oi7 


i3 


01 


9-994397 


•34 


9^2o86i9 


i3 


35 


io-79i38i 49 


12 


203797 


12 


99 


994377 


•34 


209420 


i3 


33 


790380 ! 48 


i3 


204377 


12 


96 


994337 


•34 


210220 


i3 


3i 


789780 
788982 


47 


14 


203354 


12 


94 


994336 


•34 


211018 


i3 


28 


46 


i5 


2o6i3i 


12 


92 


994316 


•34 


2ii8i5 


i3 


26 


788185 


45 


16 


206906 


12 


89 


994295 


•34 


212611 


i3 


24 


787389 


44 


I? 


207679 


12 


87 


994274 


•35 


2i34o5 


i3 


21 


786393 ; 43 1 


i8 


208432 


12 


83 


994234 


.35 


214198 
2149^9 


i3 


19 


785802 


42 


19 


209222 


12 


82 


994233 


.35 


i3 


17 


785011 


41 


20 


209992 


12 


80 


994212 


.35 


215780 


i3 


i5 


784220 


40 


21 


9-210760 


12 


78 


9-994191 


.35 


9-216568 


i3 


12 


10^783432 


ll 


22 


2ll526 


12 


75 


994171 


.35 


217356 


i3 


10 


782644 


23 


212291 


12 


73 


994 1 5o 


.35 


218142 


i3 


08 


781858 


37 


24 


2i3o55 


12 


71 


994129 


.35 


218926 


i3 


o5 


781074 i 36 


25 


2i38i8 


12 


68 


994108 


.35 


219710 


i3 


o3 


780290 35 


26 


214379 
215338 


12 


66 


994087 


.35 


220492 


i3 


01 


779508 34 
778728 33 


27 


12 


64 


994066 


.35 


221272 


12 


99 


28 


216097 


12 


61 


994043 


.35 


222032 


12 


97 


777948 1 32 


29 


216854 


12 


59 


994024 


• 35 


222830 


12 


94 


777170 i 3i 


3o 


217609 


12 


57 


9Q4oo3 


.35 


2236o6 


12 


92 


776394 j 3o 


3i 


9-218363 


12 


55 


9.993981 


.35 


9-224382 


12 


90 


io^7756i8 29 


32 


219116 


12 


53 


993960 


.35 


223156 


12 


88 


774844 


28 


33 


219868 


12 


5o 


993939 


.35 


225929 


12 


86 


774071 


27 


34 


2206.8 


12 


48 


993918 


.35 


226700 


12 


84 


773300 


26 


35 


22i367 


12 


46 


993M96 


• 36 


227471 


12 


81 


772329 1 23 


36 


2221l5 


12 


44 


993875 


• 36 


228239 


12 


79 


771761 ; 24 


37 


222S61 


12 


42 


993854 


• 36 


229007 


12 


77 


770993 


23 


38 


223606 


12 


39 


993832 


• 36 


229773 


12 


75 


770227 


22 


39 


224349 


12 


37 


99381 1 


.36 


23o539 


12 


73 


769461 


21 


40 


223092 


12.35 


993789 


•36 


23l302 


12 


71 


20 


41 


9-225833 


12-33 


9-993768 


• 36 


9-232065 


12 


69 


10.767935 


\l 


42 


226573 


12-3l 


993746 


•36 


232826 


12 


67 


767174 


43 


22731 1 


12-28 


993725 


•36 


233586 


12 


65 


766414 ! 17 


44 


22^^048 


12-26 


993703 


•36 


234343 


12 


62 


765655 ! 16 


45 


228784 


12-24 


993681 


• 36 


235 io3 


12 


60 


764897 j 1 5 


46 


229318 


12-22 


993660 


•36 


235SJ9 


12 


58 


764141 1 i4 


47 


230232 


12-20 


993638 


• 36 


236614 


12 


56 


763386 ! i3 


48 


230984 


12-18 


993616 


-36 


23^368 


12 


34 


762632 ! 12 


49 


231714 


12-16 


993394 


•37 


238120 


12 


52 


761880 II 


5o 


2 32444 


12-14 


993372 


•37 


238872 


12 


5o 


761 128 1 ID 


5. 


9-233172 


12-12 


9-993550 


• 37 


9-239622 


12 


48 


10.760378 


t 


52 


233899 


12 09 


9ry3328 


•37 


240371 


12 


46 


750629 
758882 


53 


234623 


12-07 


993306 


•37 


241118 


12 


44 


7 


54 


235349 


I2-o5 


993484 


•37 


241865 


12 


42 


738135 


6 


55 


236073 


12-03 


993462 


•37 


242610 


12 


.40 


757390 ' 5 


56 


236795 


12-01 


993440 


•37 


243354 


12 


-38 


736646 ' 4 


57 


2373l5 


n-99 


993418 


.37 


244097 


12 


-36 


755903 3 


58 


23^^235 


11-97 


993396 


•37 


244839 


12 


•34 


755161 2 


59 


53M953 


1 "-95 


993374 


.37 


243379 


12 


-32 


734421 1 


60 


239670 


1 11-93 


993351 


•37 


246319 


12-30 


753681 




Coaine 


[_J 


0. 


Sine 




Cot<anff. 


D. 


Tan^. 1 M. 



(80 DEGREES.) 



28 



(10 DEGKEES.) A TABLE OF LOGARITITMIC 



M. 


Sine 


I). 


Cosine 


D. 


Tang. 


D. 


Cotang. 


6a 


o 


9-239670 
240386 


11.93 


Q-993351 


.37 


9.246319 


12-30 


10.753681 


I 


\\X 


993329 


•37 


247057 


12.28 


752943 


5? 


2 


24MOI 


993307 


•37 


247794 


12.26 


752206 


3 


24I8I4 


11.87 


993285 


■37 


248530 


12 24 


751470 


57 


4 


242526 


11-85 


9q3262 


•37 


249264 


12-22 


750736 i 56 


5 


243237 


11-83 


993240 


-37 


Itifo 


12-20 


75oooa ! 55 


6 


243947 


1 1. 81 


993217 


-38 


12-18 


749270 


54 


I 


244656 


11.79 


993195 


■ 38 


251461 


12-17 


748539 


53 


245363 


11.77 


993172 


-38 


252191 


12-15 


747809 


52 


' 9 


246069 
246775 


11-73 


993149 


-38 


252920 


12-13 


747080 


5i 


IC 


11-73 


993127 


-38 


253648 


12-11 


746352 


5o 


II 


9-247478 


11-71 


9-993104 


-38 


9-254374 


12-09 


10-745626 


it 


12 


248181 


11-69 


993081 


-38 


255ioo 


12-07 


744900 


i3 


248883 


11-67 


993059 


-38 


255824 


12-05 


744176 


47 


14 


249583 


11-65 


993o36 


-38 


256547 


12-03 


743453 


46 


i5 


250282 


11-63 


99301 3 


•38 


257269 


12-01 


742731 


45 


i6 


250980 


II-6I 


992990 


-38 


297990 


12-00 


742010 


44 


17 


251677 


Wit 


992967 


-38 


208710 


11-98 


741290 


43 


18 


252373 


992944 


-38 


259429 


11-96 


740571 


42 


19 


253067 


11-56 


992921 


.38 


260146 


n-94 


739854 


41 


20 


253761 


11-54 


992898 


-38 


260863 


11-92 


739137 


40 


21 


9-254453 


11-52 


9-992875 


.38 


9-261578 


\IX 


10-738422 


39 


*2 


255144 


11-50 


992852 


• 38 


262292 


737708 


38 


23 


255834 


11-48 


992829 


•39 


263oo5 


11-87 


736995 


37 


24 


256523 


11-46 


992806 


.39 


263717 


11-85 


736283 


36 


25 


25721 1 


11-44 


992783 


.39 


264428 


11-83 


735572 


35 


26 


257898 


11-42 


992759 


•39 


265i38 


11-81 


734862 


34 


11 


258583 


11-41 


992736 


.39 


265847 


\]:]l 


734153 1 33 


259268 


11-39 


992713 


•39 


266555 


733445 


32 


29 


259951 


11-37 


992690 


.39 


267261 


11-76 


732739 


3i 


So 


260633 


11-35 


992666 


.39 


267967 


11-74 


732033 


3o 


3i 


9.261314 


11-33 


9-992643 


•39 


9-268671 


11.72 


10-731329 


29 


32 


261994 


ii-3i 


992619 


•39 


269375 


11-70 


73o62D 28 


33 


262673 


11-30 


992596 


.39 


270077 


11-69 


729923 


27 


34 


2633DI 


11-28 


992572 


.39 


270779 


11-67 


729221 


26 


35 


264027 


11-26 


992349 


.39 


27U79 


11-65 


72<S521 


25 


Zb 


264703 


11-24 


992525 


.39 


272178 


n-64 


727822 


24 


37 


265377 


11-22 


992501 


.39 


272876 


11-62 


727124 


23 


38 


26605 I 


11-20 


992478 


.40 


273573 


11 -60 


726427 


22 


39 


266723 


11-19 


992454 


.40 


274269 


11-58 


725731 


21 


40 


267395 


11-17 


992430 


.40 


274964 


11-57 


725o36 


20 


41 


9.268065 


ii-i5 


9-992406 


-40 


9-275658 


11.55 


10.724342 


\t 


42 


268734 


ii-i3 


992382 


• 40 


276351 


11-53 


723649 


43 


269402 


11-11 


992359 


.40 


277043 


ii-5i 


722957 


17 


44 


270069 


n-io 


992335 


.40 


277734 


ii-5o 


722266 


16 


45 


27073d 


11-08 


992311 


•40 


278424 


11-48 


721576 


i5 


46 


271400 


11-06 


992287 


-40 


279113 


11-47 


120887 14 


47 


272064 


ii-o5 


992263 


• 40 


279»oi 


11-45 


720199 1 i3 


48 


272726 


1 1 -03 


992239 


•40 


280488 


11-43 


7Io5l2 12 

718826 11 


49 


273388 


II-OI 


992214 


-40 


281174 


11-41 


5o 


274049 


10-99 


992190 


.40 


281858 


11-40 


718142 


10 


5i 


9-274708 


10.98 


9-992166 


.40 


9-282542 


11-38 


10-717458 


t 


52 


275367 


10-96 


992142 


.40 


2832 25 


11-36 


716775 


53 


276024 


10-94 


992117 


.41 


283907 


11-35 


716093 


7 


54 


2766S1 


10-92 


992093 


•41 


284588 


11-33 


715412 1 6 1 


55 


277337 


10-91 


992069 


•41 


285268 


ii-3i 


7U732 


5 


56 


277991 


10-89 


992044 


•41 


285947 


11 -3o 


714053 


4 


5-7 


278644 


10-87 


992020 


.41 


286624 


11-28 


713376 


3 


5S 


279297 


10-86 


991996 


•41 


287301 


11-26 


712699 

712023 


2 


59 


IK 


10.84 


991971 


•41 


287977 


li-25 


I 


60 


10-82 


991947 


.41 


288652 


11-23 


711348 





1 


Cosiue 


D. 


Slue ! 


_CoUuig. ^ 


D. 


Tang. 



(79 DEGREES.) 



SINES AND TANGENa"S. (11 DEGREES.) 



29 



M. 


Sine 


D. 


Cosine 


D. 


Ti'ng. 


D. 


Cotaug. 







9.280599 


10.82 


9.9Q1947 


41 


9-288652 


11-23 


10-711348 


60 


I 


281248 


10 


81 


9919^2 
991897 


41 


289326 


11-22 


710674 


S 


a 


281897 


10 


79 


41 


289999 


11-20 


710001 


3 
4 


282544 
283190 


10 
10 


]l 


991873 
991848 


41 
41 


290671 
291342 


11.18 
11-17 


]^IU 


u 


5 


283836 


10 


74 


991823 


41 


292013 


11-15 


707987 55 1 


6 


284480 


10 


72 


991799 


41 


292682 


11-14 


707318 


54 


? 


285124 


10 


71 


991774 


42 


293350 


11-12 


7o665o 


53 


985766 


10 


69 


991749 


42 


294017 


ii-ii 


705983 
705316 


52 


9 


286408 


10 


67 


991724 


42 


294684 


11-09 


5i 


10 


287048 


10 


66 


991699 


42 


295349 


11.07 


704651 


5o 


II 


9-287687 


10 


64 


9-991674 


42 


9-296013 


11-06 


10-703987 


ii 


12 


283326 


10 


63 


991649 


42 


296677 


11-04 


703323 


i3 


288964 


10 


6x 


991624 


42 


297339 


ii-o3 


702661 


47 


14 


289600 


10 


ll 


991599 


42 


298001 


II-OI 


]v,m 


46 


i5 


290236 


10 


991574 


42 


298662 


11-00 


45 


i6 


290870 


10 


56 


991549 


42 


299322 


10.98 


700678 


44 


n 


291504 


10 


54 


99>524 


42 


299980 


10-96 


700020 


43 


i8 


292137 
292768 


10 


53 


991493 


42 


3oo638 


10-95 


699362 


42 


19 


10 


5i 


991473 


42 


301295 


10-93 


698705 


41 


20 


593399 


10 


5o 


991448 


42 


301901 


10-92 


698049 


40 


21 


9-294029 
294608 


10 


48 


9-991422 


42 


9.302607 


10-90 


10-697393 


ll 


22 


10 


46 


991397 


42 


3o326i 


10-89 


696739 


23 


290286 


10 


45 


991372 


43 


3o39i4 


10-87 

10-86 


696086 


37 


24 


290913 


10 


43 


991346 


43 


304567 


695433 


36 


25 


296539 


10 


42 


991321 


43 


3oo2i8 


10-84 


694782 


35 


26 


297164 


10 


40 


991295 


43 


300869 


10-83 


6941 3 1 


34 


27 


297788 


10 


39 


991270 


43 


3o65i9 
307168 


10.81 


693481 


33 


28 


298412 


10 


ll 


991244 


43 


10-80 


692832 


32 


29 


299034 


10 


991218 


43 


307815 


10.78 


692185 


3i 


3o 


299655 


10 


34 


991 193 


43 


3o8463 


10.77 


691537 


3o 


3i 


9-300276 


10 


32 


9-991167 


43 


g. 309109 


10.75 


10-690891 


ll 


32 


300895 


10 


3i 


991 i4i 


43 


309754 


10.74 


'& 


33 


3oi5i4 


10 


29 
28 


991115 


43 


310398 


10-73 


27 


34 


302l32 


10 


991090 


43 


311042 


10-71 


688958 


26 


35 


302748 


10 


26 


991064 


43 


3ii685 


10-70 


6883 1 5 


25 


36 


3o3364 


10 


25 


991033 


43 


312327 


10-68 


687673 


24 


ll 


^S5? 


10 


23 


991012 


43 


312967 


10-67 


687033 


23 


10 


22 


990986 


43 


3i36o8 


10-65 


686392 1 22 


39 


300207 


10 


20 


990960 


43 


314247 


10-64 


685753 i 21 


40 


300819 


10 


19 


990934 


44 


3x4885 


10-62 


68511 5 


20 


41 


9-3o643o 


10 


17 


9-990908 
990882 


44 


9-315023 


io-6i 


10-684477 


19 


42 


307041 


10 


16 


44 


3i6i59 


10- 60 


683841 


18 


43 


307600 


10 


14 


990355 


44 


316795 


10-58 


683205 


\l 


44 


308259 


10 


i3 


990829 


44 


3 17430 


10.57 


682570 


45 


3o8367 


10 


II 


. 990803 


44 


318064 


10-55 


681936 
68i3o3 


i5 


46 


309474 


10 


10 


990777 


44 


318697 


10-54 


14 


^l 


3ioo3o 


10 


08 


990750 


44 


319329 


10-53 


680671 


i3 


48 


3 1 0685 


10 


07 


990724 


44 


319961 


10-51 


680039 


12 


49 


311289 
311893 


10 


o5 


990697 


44 


320092 


io-5o 


679408 ' II 


5c 


10 


04 


990671 


44 


321222 


10-48 


678778 i 10 


5i 


9 312493 


• 10 


o3 


9-990644 


44 


9-32i85i 


10-47 


10-678149 1 9 


52 


3 1 3097 
3.3698 


10 


01 


990618 


44 


322479 


10-45 


677521 1 8 


53 


10 


00 


990591 


44 


323io6 


10-44 


676894 1 7 
67626"' 6 


54 


3(4297 


9 


98 


990565 


44 


323733 


10-43 


55 


314897 


9 


97 


99o538 


44 


324353 


10-41 


670642 5 


56 


310495 


9 


96 


9905 n 


45 


324953 


10-40 


675017 / 4 


57 


3!6Dq2 


9 


94 


9904^0 


45 


320607 


10-39 


674393 1 3 


53 


3 16639 


9 


93 


990453 


45 


326231 


10-37 


673769 i 2 


5'9 


317284 


9 


91 


9904 3 1 


45 


326853 


10-36 


673147 1 1 


6o 


317879 


9.90 


9904 4 


45 


327475 


10-35 


672520 ; 


r:. 


Cosin3 


D. 


Sine 




Cotuiie. 


D. 


Tan?. 


M. 1 



(78 DEGREES,) 



30 



(12 DEGREES., A TABLE OF LOGARITHMIC 



M.l 


SiLO 


D. 


Cosine 


D. 


Tanor- 


D. 


Cotang. 1 


o 


'tl^t 


9-90 


9-990404 1 


45 


9-327474 


10-35 


10-672526 i 60 


I 


9 


88 


990378 


45 


328095 


10 


33 


671905 ! DQ 


3 


3igo66 


9 


87 


99035 1 


45 


32S7,5 


10 


32 


671285 1 58 


3 


3io658 


9 


86 


990324 


45 


329334 


10 


3o 


670666 57 


4 


320249 


9 


84 


990297 ■ 


45 


329953 


10 


29 


670047 ! 56 


5 


320840 


9 


83 


990270 


45 


33o57c 


10 


28 


669430 55 
66881 3 54 


6 


321430 


9 


82 


990243 : 


45 


351187 


10 


26 


I 


322019 


9 


80 


990215 


45 


33iHo3 


10 


25 


668197 


53 


322607 


9 


79 


990188 , 


45 


3 3241 8 


10 


24 


667582 


52 


9 


325r94 
323780 


9 


77 


990161 • 


45 


3 ?3o33 


10 


23 


666967 


5i 


10 


= 


76 


990>34 ! 


45 


333646 


10 


21 


666354 


5o 


n 


9-324366 


9 


75 


9-990107 


46 


5 334259 


10 


20 


io.665i4i 


-^2 
48 


12 


324950 


9 


73 


990079 


46 


3i4S7l 


10 


'9 


665 1 29 
664518 


i3 


325534 


9 


72 


99)o52 ! 


46 


3354H2 


10 


• 7 


47 


14 


3261 17 


9 


70 


990025 


46 


3 56093 


10 


16 


663907 


46 


i5 


326700 


9 


69 


9^Q997 


46 


336702 


10 


i5 


603298 


45 


i6 


327281 


9 


68 


9Syo-o 


46 


33i3ii 


10 


i3 


662689 


44 


17 


327862 


9 


66 


9^9942 


46 


33^9,9 


10 


12 


662081 


43 


i8 


328442 


9 


65 


9^9913 


46 


33S527 


10 


II 


661473 


42 


19 


329021 


9 


64 


989S87 


46 


339133 


10 


10 


660867 


41 


20 


329599 


9 


62 


989S60 


46 


339739 


10 


08 


660261 


40 


21 


9-330176 


9 


61 


9.989832 


46 


9-346344 


10 


07 


10.639636 


3§ 


22 


330753 


9 


60 


9S9S04 


46 


340948 


10 


06 


639032 


23 


33 1 329 


9 


58 


9^9111 


46 


34i5d2 


10 


04 


658448 


37 


24 


33 1903 


9 


57 


989749 


47 


342155 


10 


o3 


637845 


36 


25 


332478 


9 


56 


9>^972l 


47 


342737 


10 


02 


637243 


35 


26 


333o5i 


9 


54 


989693 


47 


343358 


10 


00 


636642 


34 


11 


333624 


9 


53 


9S9665 


47 


343958 


9 


^ 


636042 


33 


334195 


9 


52 


989637 


47 


344558 


9 


655442 


32 


29 


334766 


9 


5o 


989609 


^7 


343157 


9 


97 


654843 


3i 


So 


335337 


9 


49 


989582 


47 


343755 


9 


96 


634245 


3o 


3i 


9-335906 


9 


48 


9.9S9553 


47 


9-346353 


9 


94 


10-653647 


11 


32 


336475 


9 


46 


9^'9525 


47 


34^949 


9 


93 


653o3i 


33 


337043 


9 


45 


9S9497 


47 


347543 


9 


92 


652455 


U 


34 


337610 


9 


44 


9^9469 


47 


348141 


9 


91 


65 1 839 


35 


338176 


9 


43 


9'^944i 


47 


34S735 


9 


90 

88 


631265 


25 


36 


338742 


9 


41 


9^9413 


47 


349329 


9 


65o67i 


24 


11 


339306 


9 


40 


9^'9384 


47 


319922 


9 


87 


630078 


23 


'339871 


9 


39 


989356 


47 


33o5i4 


9 


86 


649486 
648M94 


23 


39 


340434 


9 


37 


9S9328 


47 


331106 


9 


85 


21 


40 


340996 


9 


36 


989300 


47 


351697 


9 


83 


6483o3 


00 


41 


9-341558 


9 


35 


9.989271 


47 


9-3322S7 


9 


82 


10-647713 


'2 


42 


3421 19 


9 


34 


9H9243 


47 


332876 


9 


81 


647124 


18 


43 


342679 


9 


32 


9^9214 


47 


353465 


9 


80 


646535 


n 


44 


343239 


9 


3i 


9S9186 


47 


334033 


9 


79 


643947 


16 


45 


343797 


9 


3o 


989137 
989128 


47 


334640 


9 


77 


645360 


i5 


46 


344355 


9 


29 


48 


33^227 


9 


^6 


644773 


i4 


47 


344912 


9 


27 


9S9100 


48 


3 3381 3 


9 


75 


644187 


i3 


48 


345469 


9 


26 


98qo7 I 


48 


3Vi398 


9 


74 


643602 


12 


49 


346024 


9 


25 


9^9042 


48 


3369S2 


9 


73 


643018 11 i 


5o 


346579 


9 


24 


989014 


48 


357366 


9 


71 


642434 


10 


5i 


9-347134 


9 


22 


9.988985 


48 


9-358149 


9 


70 


10 -641851 


i 


52 


347687 


9 


21 


9SS956 


48 


338731 


9 


69 
68 


641269 


53 


348240 


9 


20 


9889^7 


48 


339313 


9 


640687 


I 


54 


348792 


9 


19 


988898 


48 


339S93 


9 


67 


640107 


55 


349343 


9 


17 


988869 


48 


360474 


9 


66 


639526 


5 


56 


349^93 


9 


16 


988840 


48 


36I033 


9 


65 


63S947 


4 


u 


350443 


9 


i5 


Q88811 


49 


36i632 


9 


63 


638368 3 


350992 


9 


14 


9N8782 


49 


3622 10 


9 


62 


6J-'790 i a 


59 


35i54o 


9 


i3 


988753 


49 


362787 


9 


61 


63-213 ' I 


66 


352088 


9-11 


9S8724 1 


49 


363364 


9-6o 


636636 


1 




Cosine 


J). 


Sine 1 




Cotanj;. 


r 


). 


Taixg. 


;_^j 



(77 DEGREES.) 



SINES AND TANGENTS. (13 DEGKEES.) 



31 



f^" 


Sine 


D. 


CosiuPi 


D. 


Tang. 


D. 


Cotang. 




9.352088 


911 


Q 9^'^724 


49 


9-363364 


9-60 


10.636636 


60 


I 


352635 


9 


10 


988695 


49 


368940 


9 


59 


686060 1 5q 
635485 1 58 


2 


353i8i 


9 


oq 


988666 


49 


3645 1 5 


9 


58 


3 


353726 


9 


08 


988636 


49 


365o90 


9 


57 


684910 ; 57 


4 


354;?! 


9 


07 


988607 


49 


365664 


9 


55 


634336 1 56 





354815 


9 


o5 


988578 


49 


366237 


9 


54 


633768 1 55 


6 


35535S 


9 


04 


988548 


49 


366810 


9 


53 


688190 1 54 


I 


355goi 


9 


o3 


988019 


49 


367382 


9 


52 


682618 1 53 


356443 


9 


02 


988489 


49 


367953 


9 


5i 


682047 : 52 


9 


356q84 


t 


01 


988460 


49 


368524 


9 


5o 


681476 


5i 


10 


357524 


99 


988430 


49 


369094 


9 


49 


680906 


5o 


II 


9.358064 


8 


9S 


g. 98840 I 


49 


9-369653 


9 


48 


io-63o337 


49 


12 


3586o3 


8 


97 


98S371 


49 


3-'o232 


9 


46 


629768 


48 


i3 


359141 


8 


96 


988342 


49 


370799 


9 


45 


629201 
628633 


46 


14 


359678 


8 


95 


988312 


5o 


371867 


9 


44 


i5 


36021 5 


8 


93 


98^282 


5o 


371933 


9 


43 


628067 


45 


l6 


36oi52 


8 


92 


98«212 


5o 


372499 


9 


42 


627501 


44 


n 


3612^7 


8 


91 


988223 


5o 


373r64 


9 


41 


626986 
626871 


43 


i8 


361M22 


8 


% 


9S8I93 


5o 


878629 
374193 


9 


40 


42 


19 


362356 


8 


988163 


5o 


9 


89 


625807 


41 


20 


362S89 


8 


88 


988133 


5o 


374756 


9 


38 


625244 


40 


21 


9-363422 


8 


87 


9.988103 


5o 


9-375319 


9 


37 


10.624681 


U 


22 


363954 


8 


85 


98S073 


5o 


375881 


9 


35 


624119 
623558 


23 


364485 


8 


84 


988043 


5o 


376442 


9 


34 


37 


24 


365oi6 


8 


83 


988018 


5o 


877008 


9 


33 


622997 


36 


25 


3b5546 


8 


82 


9S7983 


5o 


377563 


9 


32 


622487 


35 


26 


366075 


8 


81 


987953 


5o 


378122 


9 


3i 


621878 


34 


27 


366604 


8 


80 


9 -(792 2 


5o 


378681 


9 


3o 


621819 


33 


28 


367i3i 


8 


79 


987S92 


5o 


879289 


9 


l^ 


620761 


32 


?9 


361619 


8 


77 


9S7S62 


5o 


879197 


9 


620208 


3i 


3o 


368i85 


8 


76 


987832 


5i 


38o354 


9 


27 


619646 


3o 


3i 


9-368711 


8 


75 


9.987801 


5i 


9-380910 


9 


10 


10-619090 


29 


32 


36q236 


8 


74 


987771 


5i 


381466 


9 


25 


618534 28 


33 


369-61 


8 


73 


9H7740 


5i 


382020 


9 


24 


617980 ; 27 


34 


370285 


8 


72 


9877 '0 


5i 


382575 


9 


23 


617425 26 


35 


370S08 


8 


71 


9H7679 


5i 


383129 


9 


J2 


616871 25 


36 


37i33o 


8 


70 


95-649 


5i 


383682 


9 


21 


616818 , 24 


il 


371852 


8 


69 


9S7618 


5i 


384234 


9 


20 


615766 j 23 


38 


372373 


8 


67 


987588 


5i 


384786 


9 


;? 


6i52i4 22 


39 


372894 


8 


66 


987557 


5i 


385337 


9 


614668 21 


40 


373414 


8 


65 


987526 


5i 


385888 


9 


17 


614112 20 


41 


9.373933 


8 


64 


9-987496 


5i 


9-386438 


9 


i5 


io-6i3562 19 
6i3oi3 1 18 


42 


3744D2 


8 


63 


987465 


5i 


386987 


9 


14 


43 


374970 


8 


62 


987434 


5i 


387D36 


9 


i3 


612464 i 17 


44 


375487 


8 


61 


987403 


52 


388084 


9 


12 


611916 16 


45 


37Coo3 


8 


60 


987372 


52 


388631 


9 


II 


611J69 ' i5 


46 


376519 


8 


59 


9B734I 


52 


889118 


9 


ID 


610822 ; 14 


s 


377035 


8 


58 


987310 


52 


389724 


9 


S 


610276 i3 


377549 


8 


57 


987279 
9^7248 


52 


390270 


9 


609780 1 12 


49 


378063 


8 


56 


52 


•390815 


9 


07 


609185 
608640 


II 


5o 


378577 


8 


54 


987217 


52 


391860 


9 


06 


10 


5i 


9.3^0089 


8 


53 


9.987186 


52 


9.391908 


9 


o5 


10-608097 


t 


52 


379601 


8 


52 


987155 


52 


892447 


9 


04 


607553 


53 


38oii3 


8 


5i 


987124 1 


02 


892989 


9 


o3 


607011 


7 


54 


380624 


8 


5o 


987092 


52 


393081 


9 


02 


606469 


6 


5- 


38ii34 


8 


49 


987061 


52 


894078 


9 


01 


605927 


5 


5t 


38(643 


8 


48 


987030 


52 


894614 




00 


6o5386 


4 


U 


382152 


8 


47 


986998 


52 


890154 


8 


^ 


604846 


3 


38^661 


8 


46 


986967 


52 


890694 


8 


604806 


2 


59 


383 168 


8 


45 


986986 


52 


396233 


8 


07 


608767 


I 


60 


383675 


8-44 


986904 


-52 


396771 


8-96 


608229 





' Cosine 


D. 


Si-e 




Cotanor. 


D. 


Tang. 


^L 



'ii<0 



(76 DEGREES.) 



82 



(14 DEGEEES.) A TABLE OF LOGARITHMIC 






Sire 


T). 


Cosine 


J). 


Taiig. 


D. 


Cotong. 1 


9-383675 


8-44 


'■^4 


-52 


9.396771 


8.96 


10-603229 ' 60 


I 


384182 


8 


•43 


.53 


397309 


8 


96 


602691 I 59 


3 


384687 


8 


•42 


986S41 


• 53 


3^7846 


8 


95 


602 1 54 


58 


3 


385i92 


8 


41 


986S09 
986778 


.53 


398383 


8 


94 


601617 


57 


4 


385697 


8 


40 


-53 


3989.^ 


8 


93 


^01081 


56 


5 


386201 


8 


39 


986746 


.53 


399455 


8 


92 


600545 


55 


6 


386704 


8 


38 


986714 


.53 


399990 
4oo524 


8 


9' 


600010 


54 


7 


387207 


8 


37 


9S6683 


-53 


8 


r. 


m' 


53 


8 


387709 


8 


36 


986651 


-53 


401058 


8 


52 


9 


388210 


8 


35 


986619 


.53 


401591 


8 


88 


598409 


5i 


10 


3887 1 1 


8 


34 


986087 


-53 


402124 


8 


87 


597876 


5o 


11 


9-389211 


8 


33 


9.986555 


-53 


9.402656 


8 


86 


10.597344 


^ 


12 


3897 1 1 


8 


32 


986523 


.53 


403187 


8 


85 


596813 


i3 


390210 


8 


3i 


986491 


.53 


403718 


8 


84 


596282 


47 


14 


390708 


8 


3o 


986439 


• 53 


404240 


8 


83 


595751 


46 


i5 


391206 


8 


28 


986427 


.53 


404778 


8 


82 


593222 


45 


i6 


391703 


8 


27 


986395 


-53 


4o53o8 


8 


81 


594692 


44 


\l 


392195 
39269D 


8 


26 


986363 


•54 


405836 


8 


80 


594164 


43 


8 


25 


986331 


•54 


406364 


8 


]l 


593636 


42 


19 


lllsi 


8 


24 


986299 


•54 


406892 


8 


593108 


41 


20 


8 


23 


986266 


.54 


407419 


8 


77 


592581 


40 


21 


9.394179 


8 


22 


9.986234 


•54 


9-407945 


8 


76 


10.592055 


39 


22 


394673 


8 


21 


9S6202 


•54 


408471 


8 


75 


591529 


38 


23 


395166 


8 


20 


986169 


-54 


408997 
409521 


8 


74 


591003 


ll 


24 


395658 


8 


li 


986137 


-54 


8 


H 


590479 


25 


396150 


8 


986104 


•54 


410045 


8 


73 


589953 


35 


26 


396641 


8 


17 


986072 


•54 


410569 


8 


72 


589431 
588908 


34 


11 


397132 


8 


17 


986039 


•54 


41 1092 


8 


71 


33 


397621 


8 


16 


986007 


•54 


4ii6i5 


8 


70 


588385 


32 


29 


398111 


8 


r5 


983974 


.54 


412137 


8 


69 


587863 


3i 


3o 


398600 


8 


14 


983942 


•54 


412658 


8 


68 


587342 


3o 


3i 


9.399088 


8 


i3 


9-985909 


.55 


9-4i3i79 


8 


u 


10.586821 


29 
28 


32 


399575 


8 


12 


983876 


-55 


413699 


8 


586301 


33 


400062 


8 


II 


985843 


.55 


414219 
414738 


8 


65 


585781 


ll 


34 


400349 


8 


10 


983811 


• 55 


8 


64 


583262 


35 


401 o3d 


8 


^i 


983778 


• 55 


4i5257 


8 


64 


584743 


25 


36 


401320 


8 


983745 


• 55 


415775 


8 


63 


584225 


24 


37 


4o2oo5 


8 


07 


985712 


• 55 


416293 


8 


62 


583707 


23 


38 


402489 


8 


06 


985679 


.55 


416810 


8 


61 


583190 


22 


39 


402972 


8 


o5 


985646 


• 55 


417326 


8 


60 


582674 


21 


40 


403455 


8 


04 


9856i3 


.55 


417842 


8 


59 


582158 20 1 


41 


9.403938 


8 


o3 


9.985580 


-55 


9-418358 


8 


58 


10.581642 


\t 


42 


404420 


8 


02 


983347 


.55 


418873 


8 


ll 


581127 


43 


4o4qoi 


8 


01 


985514 


-55 


419387 


8 


58o6i3 


17 


44 


405382 


8 


00 


985480 


-55 


419901 


8 


55 


580009 , 16 1 


.^5 


4o5862 




9^ 


985447 


-55 


420413 


8 


55 


579585 


i5 


46 


406341 




985414 


-56 


420927 


8 


54 


579073 
57a^6o 


14 


47 
48 


406820 




97 


985380 


• 56 


421440 


8 


53 


i3 


407299 




96 


985347 


• 56 


421952 


8 


52 


578048 


n 


49 


407777 




95 


985314 


-56 


422463 


8 


5i 


577537 


ir 


5o 


408254 


n 


94 


985280 


• 56 


422974 


8 


5o 


577026 


10 


5i 


9.408731 




94 


9.985247 


• 56 


9.423484 


8 


it 


10.576516 


I 


5s 


409207 


7 


93 


983213 


• 56 


423993 


8 


576007 


53 


409682 




92 


985180 


-56 


424303 


8 


48 


575497 
574989 


I 


54 


410157 




91 


983146 


-56 


423011 


8 


47 


55 


4io632 




i 


983113 


-56 


425519 


8 


46 


574481 


b 


56 


411106 




983079 


• 56 


426027 


8 


45 


573973 


4 


u 


41 1379 




983043 


• 56 


426534 


8 


44 


573466 


3 


412052 




!i 


98301 1 


-56 


427041 


8 


43 


572930 
572453 


a 


59 


412524 




984978 


• 56 


427547 


8 


43 


I 


66 


412996 


7^85 


984944 


•56 


428052 


842 


571948 





Cosine 


D. 


Sine 


1 Cotanor. 


D. 


Tang. 


Lmu 



(75 DEGREES.) 



SINES AND TANGENTS. (15 DEGREES.) 



33 



n. 


Sine 


D. 


Cosine j 


D. 


Tang. 


D. 


Cotuilg. 


o 


9 412996 


7-85 


9 984944 


W 


9.428052 


8.42 


10-571948 1 60 


I 


^ 413467 


7-84 


984910 
984876 


•57 


428557 


8 


41 


571443 ■ 5q 


a 


413938 


7-83 


•57 


429062 


8 


40 


570933 1 58 


3 


414408 


7-83 


984S42 


•57 


429566 


8 


ll 


570434 1 57 


4 


414878 


7-82 


984808 


•57 


430070 


8 


569930 56 


5 


415347 


7-81 


984774 


•57 


430573 


8 


38 


569427 


55 


6 


4i58i5 


7-8o 


984740 


'V 


431075 


8 


37 


568925 


54 


I 


416283 


?:?? 


984706 


•57 


43 1 577 


3 


36 


568423 


53 


416731 


984672 


•57 


432079 


8 


35 


567921 


52 


9 


417317 


7-77 


984637 


'P 


432580 


8 


34 


567420 1 5i 


10 


• 417684 


7-76 


984603 


•57 


433080 


8 


33 


566920 1 5o 


II 


9'4i8i5o 


7-75 


9.984369 


•57 


9.433580 


8 


32 


10-566420 


8 


IS 


4i86i5 


7-74 


984535 


•57 


434080 


8 


32 


560920 


i3 


419079 


7-73 


984300 


•57 


434579 


8 


3i 


565421 


47 


14 


419544 


7-73 


984466 


•57 


435078 


8 


3o 


564922 


46 


i5 


420007 


7-72 


984432 


.58 


435576 


8 


29 


564424 


45 


i6 


420470 


7-71 


984397 


.58 


436073 


8 


28 


563927 


44 


\l 


420933 
421395 


7-70 


984363 


• 58 


436570 


8 


28 


563430 


43 




984328 


.58 


437067 


8 


^1 


562933 


42 


19 


421857 
4223i8 


7-68 


984294 


.58 


437563 ■ 


8 


26 


562437 


41 


20 


7-67 


984209 


.58 


438059 


8 


25 


561941 


40 


21 


9-422778 


7.67 


9.984224 


.58 


9.433554 


8 


24 


10-561446 


It 


22 


423238 


7-66 


984190 


.58 


439048 


8 


23 


560902 


23 


423697 


7-65 


984155 


.58 


439543 


8 


23 


560437 


37 


24 


424i56 


7-64 


984120 : 


.58 


440036 


8 


22 


309964 


36 


25 


424615 


7-63 


984085 I 


.58 


440529 


8 


21 


509471 


35 


26 


420073 


7-62 


984000 


.58 


441022 


8 


20 


553978 
558486 


34 


27 


425530 


7-61 


984015 


.58 


44i5i4 


8 


19 


33 


28 


423987 


7-6o 


983981 


.58 


442006 


8 


\l 


557994 


32 


29 


426443 


7-60 


983946 


.58 


442497 
442988 


8 


5575o3 


3i 


3o 


426899 


7.59 


98391 1 


.58 


8 


17 


557012 


3o 


3i 


9-427354 


7-58 


9.983875 


.58 


9-443479 
443968 


8 


16 


10-556521 


ll 


32 


428263 


7-57 


983840 


.59 


8 


16 


556o32 


33 


7-56 


9838o5 


.59 


444458 


8 


i5 


555542 


27 


34 


428717 


7-55 


983770 


.59 


444947 


8 


*i4 


5ooo53 


26 


35 


429170 


7-54 


983735 


.59 


445435 


8 


i3 


504565 


25 


36 


429623 


7-53 


983700 1 


.39 


445923 


8 


12 


554077 


24 


II 


430075 


7-52 


983664 


.59 


44641 I 


8 


12 


553589 


23 


43o527 


7-52 


983629 


.59 


446898 


8 


II 


553102 


22 


39 


430978 


7-5i 


983594 


.59 


447384 


8 


10 


552616 


21 


40 


431429 


7.50 


983558 


.59 


447870 


8 


09 


5o2i3o 


20 


41 


9.431879 


7-49 


9.983523 


.59 


9-448356 


8 


0^ 


10 -55 1 644 


\l 


42 


432329 


7-49 


983487 


.59 


448841 


8 


55 1 1 09 


43 


432778 


7-48 


983452 


.59 


449326 


8 


07 


550674 


n 


44 


433226 


7-47 


983416 


.59 


449810 


8 


06 


500190 


16 


45 


433675 


7-46 


983331 


.59 


450294 


8 


06 


549706 


i5 


46 


434122 


7.45 


983345 


.59 


450777 


8 


o5 


540223 


14 


"^l 


434569 


7-44 


983309 


.59 


451260 


8 


04 


543740 


i3 


48 


435016 


7-44 


983273 


.60 


451743 


8 


o3 


548207 


12 


i^ 


435462 


7-43 


983238 


.60 


452225 


8 


02 


547775 


11 


5o 


435908 


7-42 


983202 


.60 


432706 


8 


02 


547294 


10 


5i 


9-436353 


7-41 


9.983166 


.60 


9-453187 


8 


01 


10 .54681 3 


I 


52 


436798 


7-40 


983 i3o 


.60 


453668 


8 


00 


546332 


53 


437242 


7-40 


983094 


.60 


454148 




99 


540832 


7 


I 54 


43:636 


7.39 
7-38 


983008 


.60 


454628 




^ 


545372 


6 


L^ 


433129 


983022 


.60 


455107 




544S93 


5 


1 56 


438072 


7-37 


982986 


.60 


455586 




97 


544414 


4 


1 Jz 


43?oi4 


7-36 


982950 


.60 


456064 




96 


543936 


3 


58 


439406 


7-36 


982914 


.60 


456542 




96 


543458 


2 


^ 


439^97 


7.35 


982878 


.60 


457019 
457496 




95 


542981 


I 


60 


440338 


7-34 


982842 


.60 


7-94 


542504 





1 1 Cosine 


1 D. 


Sine i 


Cotang. 


D. 


Tansr. 


"ST 



(74 DEGREES.) 



34 



(IG DEGREES.) A TABLE OF LOGARITHMIC 



M. 




Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotaiig. 


60 


9-440338 


7-34 


9-982842 


60 


9-457496 


7-94 


io-5425o4 


I 


440778 




33 


982805 


60 


457973 




•93 


542027 


59 
58 


2 


441 218 




32 . 


982769 


61 


458449 




•93 


54i55i 


3 


441608 




3i 


982733 


61 


458925 




92 


541075 


57 


4 


442096 




3i 


082696 


61 


439400 




9' 


540600 


56 


5 


442535 




3o 


982660 


61 


459875 




90 


540125 


55 


6 


442973 




29 


982624 


61 


460349 




90 


539631 


54 


7 


443410 




28 


982587 


61 


460823 






539177 


53 


& 


443847 




27 


982551 


61 


461297 




88 


538703 


52 


9 


444284 




27 


982014 


6i 


461770 




88 


538^30 


5i 


10 


444720 




26 


982477 


61 


462242 




87 


537758 


5o 


11 


9-445i55 




25 


9-982441 


61 


9-462714 




86 


10-537286 


49 


12 


445590 




24 


982404 


61 


463 180 




85 


536814 


48 


i3 


446025 




23 


982367 


61 


463658 




85 


536342 


47 


14 


446459 




23 


982331 


61 


464129 




84 


535871 


46 


ID 


446S93 




22 


982294 


61 


464399 




83 


535401 


45 


i6 


447326 




21 


982237 


61 


463069 




83 


534931 


44 


n 


447739 




20 


982220 


62 


463539 
.466008 




82 


534461 


43 


i8 


448191 




20 


982183 


62 




81 


533992 


42 


19 


448623 




19 


982145 


62 


466476 




80 


533524 


41 


20 


449054 




18 


982109 


62 


466945 




80 


533o55 


40 


21 


9-449485 




17 


9-982072 


62 


9-467413 




79 


io-53258y 


39 


22 


4499 '5 




16 


9S2035 


62 


467880 




78 


532120 


38 


23 


45o345 




16 


981998 


62 


468347 




78 


531653 


37 


24 


450775 




i5 


98 1 96 1 


62 


468814 




77 


531186 


36 


25 


431204 




14 


981924 


62 


469280 




76 


530720 


35 


26 


45i632 




i3 


981886 


62 


469746 




73 


530234 


34 


11 


452060 




i3 


981849 


62 


47021 1 




75 


5297H9 


33 


452488 




12 


981812 


62 


470676 




74 


529324 


32 


29 


452915 




II 


981774 


62 


47M4J 




73 


528839 


3i 


3o 


453342 


7 


10 


981737 


62 


471605 




73 


528895 


3o 


3i 


9-453768 


. 


10 


9-981699 


63 


9.472068 




72 


10-527932 


29 


32 


454194 




09 


981662 


63 


472532 




7> 


527468 


2S 


33 


454619 




08 


981625 


63 


472993 




7J 


527005 


27 


34 


455o44 




07 


981587 


63 


473437 




70 


526543 


26 


35 


455469 




07 


981549 


63 


473919 




69 


526081 


25 


36 


455893 




06 


981 5i 2- 


63 


474381 




69 


523610 


24 


37 
38 


4563 1 6 




o5 


981474 


63 


474842 




68 


525i58 


23 


456739 




04 


981436 


63 


4753o3 




67 


524697 


22 


39 


457162 




04 


98i3q9 


63 


473768 




67 


524237 


21 


40 


457584 




o3 


981861 


63 


476223 




66 


523777 


20 


41 


9 -458000 




02 


9-981323 


63 


9-476683 




65 


10 •5233 1 7 


19 


42 


458427 
458848 




01 . 


981285 


63 


477 '42 




65 


522S58 


18 


43 




01 


9B1247 


63 


477601 




64 


522899 


17 


44 


459268 




00 


981209 


63 


478059 




63 


521941 


16 


45 


45968S 


6 


99 


981171 


63 


478517 




63 


52i4>s3 


i5 


46 


460108 


6 


98 


981133 


64 


47«973 




62 


521025 


14 


47 


460527 


6 


98 


981095 


64 


479432 




61 


520368 


i3 


48 


460946 


6 


97 


981037 


64 


479f^«9 




61 


520111 n 


49 


461 364 


6 


96 


981019 


64 


480345 




60 


519635 


II 


5o 


461782 


6 


95 


980981 . 


64 


480801 




39 


519199 


10 


5) 


9.462199 


6 


95 


9.980942 


04 


9-481257 




39 


io-5i8743 


t 


5a 


462616 


6 


94 


980904 • 


64 


481712 




58 


5i82e8 


53 


463o32 


6 


93 


9S0866 • 


64 


482167 




57 


517833 


1 


54 


463448 


6 


93 


080827 • 


64 


482621 




57 


517379 


6 


55 


463864 


6 


92 


980789 • 


64 


488075 




56 


516925 


5 


56 


464279 


6 


91 


980750 • 


64 


483529 




55 


5i647i 


4 


u 


464694 


6 


90 


980-' 1 2 


64 


483982 




55 


5i6oi8 


3 


465 1 08 


6 


% 


980673 . 


64 


484435 




54 


5 15565 


2 


59 


465522 


6 


980635 • 


64 


484887 




53 


5i5ii3 


I 


1 60 


465935 


6-88 


980596 . 


64 


485339 


7^53 


5 I 4661 







Cosine 


D. 


Sine 1 


1 Cotang. 


D. 


Tau^. 


IT* 



(73 DEGREES.) 



SINES AND TANGENTS. (17 DEGREES.) 



35 



"m. 


Sine 


D. 


Cosine 


D. 


Taug. 


D. 


Coiang. 




o 


9-465935 

466348 


6-88 


9-980596 


64 


9-485339 


7-55 


io-5i466i 


60 


I 


6-88 


980558 


64 


485791 




52 


514209 ; 59 

5i3758 ; 58 


2 


466761 


6-87 


980519 


65 


486242 




5i 


3 


467173 


6-86 


980480 


65 


486693 




5i 


5 1 3307 1 57 


4 


467535 


6-85 


980442 


65 


487143 




5o 


512857 56 


5 


467996 


6-85 


980403 


65 


487593 




49 


512407 55 


6 


468407 


6-84 


980364 


65 


488043 




S 


511957 54 
5u5o8 1 53 


I 


468817 


6-83 


980325 


65 


488492 




46g227 


6-83 


980286 


65 


488941 




47 


5no59 52 , 


9 


469637 


6-82 


980247 


65 


489390 




47 


5io6io 5i 


10 


470046 


6.81 


980208 


65 


489838 




46 


510162 5o 


II 


g. 470455 


6.80 


9-980169 


65 


9-490286 




46 


io-5o97i4 40 
509267 ! 48 


12 


470863 


6-8o 


9S0130 


65 


490733 




45 


i3 


471271 


6-70 
6.78 


980091 


65 


491 180 




44 


508820 


47 


14 


47(6^9 


980052 


65 


491627 




44 


5o8373 


46 


i5 


472086 


6-78 


980012 


65 


492073 




43 


507927 


45 


i6 


472492 


6-77 


979973 


65 


492519 




43 


507481 


44 


n 


472898 


6.76 


979934 
979895 


66 


492965 




42 


5o7o35 


43 


i8 


473304 


6.76 


66 


493410 




41 


5o65go 


42 


19 


473710 


6-75 


979835 


66 


493354 




40 


506146 


41 


30 


4741 1 5 


6-74 


979816 


66 


494299 




40 


5o57oi 


40 


21 


9-474519 


6-74 


9'97'5776 


66 


9-494743 




40 


io-5o5257 


li 


22 


474923 


6-73 


979737 


66 


495186 




It 


504814 


23 


475327 


6.72 


& 


56 


495630 




504370 


37 


24 


473730 


6-72 


56 


496073 




37 


503927 


36 


25 


476133 


6-71 


979618 


66 


496515 




37 


5o3485 


35 


26 


476536 


6-70 


979579 


66 


496957 
497399 




36 


5o3o43 


34 


11 


476933 


6-69 


979539 


66 




36 


5o26oi 


33 


477340 


6-69 
6-68 


979499 


66 


497841 
498282 




35 


5o2i59 


32 


29 


477741 


979439 


66 




34 


501718 


3i 


3o 


478142 


6-67 


979420 


66 


498722 




34 


501278 


3o 


3i 


9-478542 


6.67 


g- 979380 


66 


9-499'63 




33 


io.5oo837 


ll 


32 


478942 


6.66 


979340 


66 


499603 




33 


5oo397 
499958 


33 


479342 


6-65 


979300 


67 


5ooo42 




32 


ll 


34 


479741 


6-65 


979260 


67 


5oo48i 




31 


499319 


35 


480140 


6-64 


979220 


67 


500920 
5oi359 




31 


499080 


25 


36 


480539 


6-63 


979180 


67 




30 


498641 


24 


ll 


480937 


6-63 


979 '40 


67 


501797 




30 


498203 


23 


481334 


6-62 


979100 


67 


5o2235 




It 


497765 


22 


39 


48 1 73 1 


6.61 


979059 


67 


502672 




497328 


21 


40 


482128 


6-61 


979019 


67 


5o3io9 




28 


496891 


20 


41 


g. 482525 


6-60 


9-978979 


67 


g-5o3546 




27 


10-496454 


It 


42 


482921 


6-59 


978939 
978898 


67 


503982 




27 


496018 


43 


4833 16 




67 


5o44i8 




26 


495582 


17 


44 


483712 


978858 


67 


504854 




25 


495146 


16 


45 


484107 


6^57 


978817 


67 


505289 




25 


4947 1 1 


i5 


46 


484501 


6.57 


978777 


67 


5o5724 




24 


494276 


14 


% 


484S95 


6-56 


978736 


67 


5o6i59 
506593 




24 


493841 


i3 


435289 


6-55 


978696 


68 




23 


493407 


12 


49 


485682 


6-55 


978655 


68 


507027 




22 


492973 


11 


5o 


486075 


6-54 


978615 


68 


507460 




22 


492540 


10 


5i 


9-486467 


6-53 


9-978574 


68 


9-507893 




21 


10-492107 


t 


52 


486S60 


6-53 


978533 


68 


5o8326 




21 


491674 


53 


487251 


652 


9784q3 


68 


508759 




20 


491 241 


7 


f4 


487643 


6.5i 


978452 


68 


509191 




19 


49080Q 


6 


55 


488034 


6-5i 


97841 1 


68 


509622 




\l 


490378 


5 


56 


488424 


6-5o 


978370 


68 


5ioo54 




489946 


4 


U 


488814 


6-5o 


978329 


68 


510485 




18 


4895.5 


3 


489204 


6-49 


978288 


68 


510916 
5ii346 




!^ 


489084 
488654 


a 


59 


4895^3 


6-48 


978247 


68 




I 


L, „. 


6-48 


978206 


68 


511776 


7^16 


488224 





Coskie 


D. 


Siae 


D. 


Cotano^. 


D. 


Tanc-. 


M. 



17 



(72 DEGREKS.) 



86 



(18 DEGllEES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


(!otang. 







9-489082 


6.48 


9-978206 


• 68 


9.5n776 


7.16 


10-488324 


60 


I 


490J71 


6 


-48 


978165 


-68 


512206 




16 


487794 


5? 


2 


490739 


6 


47 


978124 


-68 


512685 




i5 


487865 


3 


491147 


6 


-46 


978088 


.69 


518064 




14 


486936 
486507 


57 


4 


491535 


6 


-46 


978042 


.69 


518493 




14 


56 


5 


491922 


6 


.45 


978001 


.69 


518921 
514349 




i3 


486079 


55 


6 


492808 


6 


44 


977959 
977918 


.69 




i3 


485651 


54 


7 
6 


492695 
498081 


6 


44 


69 


514777 




12 


485223 


53 


6 


43 


977877 


69 


5i52o4 




12 


484796 


5a 


; 


493466 


6 


42 


977835 


69 


5i563i 




II 


484869 


5i 


IC 


498851 


6 


42 


977794 


69 


516057 




10 


483943 


5o 


!I 


9-494236 


6 


4i 


9-977752 


69 


9.516484 




10 


io-4835i6 


49 


12 


494621 


6 


41 


977711 


69 


516910 
517335 




09 


488090 


48 


l3 


495005 


6 


40 


977669 
977628 


69 




It 


482665 


47 


14 


49^388 


6 


39 


^ 


517761 




482239 


46 


i5 


493772 


6 


39 

38 


977586 


69 


5i8i85 




08 


48i8i5 


45 


i6 


496154 


6 


977544 


70 


518610 




07 


481890 


44 


n 


496537 


6 


37 


977508 


.70 


519084 




06 


480966 
480O42 


43 


i8 


496919 
497801 


6 


37 


977461 


.70 


519458 




06 


42 


^9 


6 


86 


977419 


-70 


519882 




o5 


480118 


41 


20 


497682 


6 


36 


977377 


70 


52o3o5 




o5 


479695 


40 


21 


9-498064 


6 


35 


9-977335 


70 


9-520728 




04 


10-479272 
478849 


ll 


22 


498444 


6 


34 


977293 


70 


52ii5i 




08 


23 


498825 


6 


34 


977231 


70 


521573 




o3 


478427 


37 


24 


499204 


6 


33 


977209 


70 


521995 




03 


478005 


36 


25 


499584 


6 


32 


977167 


70 


522417 




02 


477583 


35 


26 


499963 


6 


32 


977125 


70 


522838 




02 


477162 


34 


11 


5oo342 


6 


3i 


977083 


70 


528259 




01 


476741 


33 


500721 


6 


3i 


977041 


70 


528680 




01 


476820 


32 


29 


501099 


6 


3o 


976999 


70 


524100 




00 


475900 


3i 


3o 


501476 


6 


29 


976907 


70 


524520 


6 


99 


475480 


3o 


3i 


9-5oi854 


6 


29 


9.976914 


70 


9.524989 


6 


99 


10-475061 


It 


32 


50223l 


6 


28 


976S72 


71 


525359 


6 


98 


474641 


33 


502607 


6 


28 


976880 


71 


52577§ 


6 


98 


474222 


27 


34 


502984 
5o386o 


6 


27 


976787 


71 


526197 


6 


97 


478808 


26 


35 


6 


26 


976745 


71 


52661 5 


6 


97 


473385 


25 


36 


508785 


6 


26 


976702 


71 


527038 


6 


96 


472967 


24 


37 


5o4iio 


6 


25 


976660 


71 


527451 


6 


96 


472549 


23 


38 


5o4485 


6 


25 


976617 


71 


527868 


6 


95 


472182 


22 


39 


5o486o 


6 


24 


976574 


71 


528285 


6 


90 


471715 


21 


40 


5o5284 


6 


23 


976532 


71 


528702 


6 


94 


471298 


20 


41 


9-5o56o8 


6 


23 


9-976489 


71 


9-529119 


6 


93 


10-470881 


19 


42 


505981 


6 


22 


976446 


71 


529085 


6 


93 


470465 


18 


43 


5o6854 


6 


22 


976404 


71 


529950 


6 


93 


47oo5o 


17 


44 


506727 


6 


21 , 


976861 


71 


53o366 


6 


92 


469684 


16 


45 


507099 


6 


20 


676318 


71 


580781 


6 


91 


469219 


i5 


46 


507471 


6 


20 


976275 


71 


531196 


6 


91 


468804 


14 


47 


507848 
508214 


6 


19 


976282 


72 


531611 


6 


90 


468889 
467975 
467561 


i3 


48 


6 


;? 


976189 


72 


532025 


6 


% 


12 


49 


5o8585 


6 


976146 


72 


582489 


6 


II 


5c 


008956 


6 


18 


976108 


72 


532853 


6 


89 


467147 


.0 


5i 


9.509826 


6 


17 


9-976060 


72 


9.538266 


6 


88 


10-466734 


§ 


52 


509696 


6 


16 


976017 


72 


583679 


6 


88 


466821 


53 


5ioo65 


6 


16 


975974 


72 


534092 


6 


87 


465908 


7 


54 


510434 


6 


i5 


975980 


72 


534504 


6 


87 


465496 
465o84 


6 


55 


5io8o3 


6 


i5 


975887 


72 


534916 


6 


86 


5 


^6 


511172 


6 


14 


975844 


72 


535828 


6 


86 


464672 


4 


11 


5ii54o 


6 


18 


975800 


72 


535789 


6 


85 


464261 


3 


511907 

5l22l5 


6 


i3 


975757 


72 


536i5o 


6 


85 


463850 


5 


59 


6 


12 


975714 


72 


536561 


6 


84 


468489 
468028 


I 


66 


512642 


6-12 


975670 


72 


536972 


6 84 







Cosine 


D. 


Sine 


D. 


Cotaug. 


D. 


lang. 


Jk 



{11 DEaREES.) 



SINES AND TANGENTS. (19 DEGREES.) 



37 



M. 




SJJie 


D. 


Coiiiie 


D. 


Taag. 


D. 


Cotang. 




9.512642 


6.12 


9.975670 


73 


0-536972 


6.84 


10.4630'. 8 


60 


I 


5x3000 


6-11 


973627 


73 


537382 


6 


83 


462618 


u 


a 


513375 


6. II 


975583 


73 


537792 


6 


83 


462208 


3 


5i374i 


6-10 


975539 


73 


538202 


6 


82 


46x798 


57 


4 


514107 


6.09 


975496 


73 


53861 X 


6 


82 


461389 


56 


5 


514472 


6. 09 
6.08 


975452 


73 


539020 


6 


81 


460980 


55 


6 


5 I 483 7 


973408 


7? 


539429 


6 


8x 


460371 


54 


I 


5l5202 


6.08 


975365 


73 


539837 


6 


80 


460163 


53 


5 1 5566 


6.07 


975321 


73 


540245 


6 


80 


439733 


52 


9 


5i593o 


6.07 


975277 


'7? 


540653 


6 


79 


439347 ; 5i 1 


10 


516294 


6.06 


975233 


73 


541061 


6 


79 


458939 


5o 


II 


9.516657 


6.o5 


9.975189 


7? 


c. 541 468 


6 


78 


xo. 458532 


S 


13 


517020 


6.05 


975143 


75 


541875 


6 


78 


458x25 


i3 


5173S2 


6.04 


975101 


7^ 


542281 


6 


77 


437719 


47 


14 


517745 


6.04 


975057 


H 


■ 542688 


6 


77 


437312 


46 


i5 


518107 


6.03 


975oi3 


73 


543094 


6 


76 


436906 


45 


i6 


518468 


6 -03 


974969 


74 


543499 


6 


76 


43650X 


44 


\l 


518829 


6.02 


974923 


74 


543905 
544310 


6 


75 


436095 


43 


519190 


6.01 


974S80 


74 


6 


75 


4556Q0 
455285 


42 


19 


5i955i 


6.01 


974836 


74 


544715 


6 


74 


41 


20 


519911 


6.00 


974792 


74 


545x19 


6 


74 


45488 X 


40 


21 


9.520271 


6.00 


9.974748 


74 


9 545524 


6 


73 


10.454476 


It 


22 


52063 1 


5.99 


974703 


74 


545928 


6 


73 


454072 


23 


520990 


til 


974639 


74 


546331 


6 


72 


453669 


37 


24 


521349 


974614 


74 


546735 


6 


72 


453263 


36 


25 


521707 


5.98 


974570 


74 


547138 


6 


71 


432862 


35 


26 


522066 


5.97 


974323 


74 


547540 


6 


71 


432460 


34 


27 


522424 


5.96 


974481 


74 


547943 
548345 


6 


70 


432037 


33 


28 


522781 


5.96 


974436 


74 


6 


70 


431655 


32 


29 


523 138 


5.95 


974391 


74 


548747 


6 


69 


451253 


3i 


36 


523495 


5.95 


974347 


75 


549x49 


6 


69 


45o85x 


3o 


3i 


9.523852 


5.94 


9.974302 


75 


9.549350 


6 


68 


xo.45o45o 


It 


32 


524208 


5-94 


974257 


75 


549931 


6 


68 


450049 


33 


524564 


5.93 


974212 


75 


55o332 


6 


67 


449648 


27 


34 


524920 


5.93 


974167 


75 


550752 


6 


67 


449248 


26 


35 


525275 


5.92 


974122 


75 


55ii52 


6 


66 


448848 


25 


36 


525630 


5.91 


974077 


75 


55x552 


6 


66 


448448 


24 


u 


525984 


5.91 


974032 


75 


55x932 


6 


65 


448048 


23 


526339 


5.90 


973987 


n 


55235X 


6 


65 


447649 


22 


39 


526693 


5.90 


973942 
973897 


7^ 


552750 


6 


65 


447250 


2X 


40 


527046 


5.^9 


75 


553x49 


6 


64 


446851 


20 


41 


9.527400 


5.89 


9-973852 


75 


9-553548 


6 


64 


10.446452 


\t 


42 


527753 

528lOD 


5.88 


973807 


V 


553946 
554344 


6 


63 


446054 


43 


5.83 


973761 


75 


6 


63 


445656 X7 | 


44 


528458 


5.87 


973716 


76 


55474X 


6 


62 


445259 


x6 


45 


528810 


5.87 


973671 


76 


553139 


6 


62 


44486 X 


i5 


46 


529161 


5.86 


973625 


76 


555536 


6 


61 


444464 


14 


47 


529513 


5.86 


973580 


76 


555933 
556329 


6 


61 


444067 


x3 


48 


529864 


5.85 


973535 


76 


6 


60 


44367 X 


12 


49 


53021 5 


5.85 


973489 


76 


556725 


6 


60 


443275 


XI 


5o 


53o565 


5.84 


973444 


76 


557121 


6 


59 


442879 


10 


5i 


Q-53o9i5 


5.84 


9.973398 


76 


9.5575x7 


6 


59 


10.442483 


i 


5i 


531265 


5.83 


973332 


76 


557913 


6 


U 


442087 


53 


53i6i4 


5.82 


973307 


76 


5583o8 


6 


441692 


I 


54 


531963 
532312 


5.82 


973261 


76 


558702 


6 


58 


441298 


55 


ii' 


9732x5 


76 


539097 


6 


57 


440903 


5 


56 


532661 


5.81 


973169 


76 


55949 X 


6 


57 


440309 


4 


u 


533009 


5.80 


973x24 


76 


559885 


6 


56 


440X13 


3 


533357 


5.80 


973078 


76 


560279 
560673 


6 


56 


43972 X 


2 


59 


533704 


tl^ 


973o32 


77 


6 


55 


439327 


I 


60 


. 534002 


972986 


77 


56 I 066 


6.55 


43893J 





I. - 


Ccr'-a« 


D. 


Sine 


D. 


Cotanor. 


D. 


Taiior 1 M. 1 



(70 DEGREES.) 



'68 


(20 


DEGRE] 


Eb.; A TABLE OF LOGARITHMIo' 




~sr 


Suie 


D. 


Cosine 


D. 


Tan?. 


D. 


Cotan?. 




c 


, 9- 53403 > 


5.78 


9-972986 


•77 


' Q-56io66 


6.55 


10-43^34 


l6o* 


1 


534399 


5-77 


972940 


•77 


561459 


6-54 


433541 i 59 
438.49 1 58 


1 


534745 


5-77 


972 x>4 


•77 


56.85. 


6-54 


3 


1 535092 


5-77 


972^48 


•77 


562244 


6-53 


437-'56 1 57 
437364 i 56 


4 


535t3:i 


5.76 


972S02 


•77 


562636 


6-53 


5 


535733 


5-76 


972755 


77 


563028 


6-53 


.436972 


55 


6 


536129 


5.75 


972709 


77 


563419 


6-52 


436531 


54 


7 


536474 


5-74 


972663 


•77 


563S11 


6-52 


436.^9 


53 


S 


536Si8 


5-74 


972617 


•77 


564202 


6-5i 


435793 


52 


9 


537163 


5.73 


972070 


•77 


564592 


6-5i 


435408 


5i 


lo 


537507 


5.73 


972524 


•77 


564953 


6-50 


4350.7 


5o 


II 


9.537851 


'5-72 


9-972478 


'n 


9-565373 


6-5o 


10.434627 


it 


12 


53S194 


5-72 


972431 


.78 


565763 


6-49 


434237 


i3 


53S533 


5-71 


972 385 


.78 


566153 


6-49 


433S47 


47 


14 


538880 


5-71 


972338 


•^? 


566542 


tit 


433458 


46 


i5 


539223 


5-70 


972291 


.78 


566932 


433o63 


45 


l6 


539565 


5-70 


972245 


•''? 


567320 


6-43 


432680 


44 


n 


539907 


5-69 


972.93 


'''i 


567709 


6-47 


432291 


43 


i8 


540^49 


5-69 


972i5i 


•■'? 


563oo3 


6-47 


43.902 


42 


19 


540590 


5-68 


972105 


.78 


5634^6 


6-46 


43nj4 


41 


20 


54og3i 


5-63 


972058 


.78 


563873 


6-46 


431127 


40 


21 


9041272 


5-67 


9-97201 1 


.78 


Q. 569261 


6-45 


10-430739 


39 


22 


54.6-3 


5-67 


971964 


.78 


569648 


6-45 


43o352 


38 


23 


541953 


5-66 


97'9'7 


'l^o 


570035 


6-45 


429965 


37 


24 


542293 


5-66 


971370 


.78 


570422 


6-44 


429378 


36 


25 


542632 


5-65 


971823 


"^i 


570809 


6-44 


429191 


35 


26 


542971 


5-65 


971776 


.78 


571.93 


6-43 


4233o5 


34 


27 


5433.0 


5-64 


97.729 


•79 


57i53i 


6-43 


42S419 


33 


28 


543649 


5-64 


9716S2 


•79 


571967 
572352 


6-42 


428033 


32 


29 


543987 


5-63 


971635 


•79 


6-42 


427648 


3i 


36 


544325 


5-63 


971588 


•79 


5-72738 


6-42 


427262 


3o 


3i 


9-544663 


5-62 


9-971540 


•79 


9-573123 


6-41 


10-426S77 


It 


32 


545ooo 


5-62 


971493 


•79 


573507 


6.41 


426493 


33 


545338 


5-6i 


971446 


•79 


573892 


640 


426.08 


27 


34 


545674 


5-6i 


971398 


•79 


574276 


6-40 


425724 


26 


35 


546011 


5.60 


971351 


•79 


574t)6o 


6-39 


425340 


25 


36 


546347 


5-60 


97i3o3 


•79 


575044 


6-39 


424956 


24 


37 


546683 


5-59 


971256 


•79 


575427 


6-39 


424573 


23 


33 


5470«9 


5-59 


971208 


•79 


57d3io 


6-38 


424190 


23 


39 


547^54 


5-58 


971161 


•79 


576.93 


6-38 


423307 


21 


40 


5476^9 


5-58 


971113 


•79 


576576 


6-37 


423424 


20 


41 


9.548024 


5-57 


9-971066 


.80 


9-576953 


6-37 


10-42304! 


•9 


42 


548359 
548693 


5.57 


971018 


.80 


577341 


6-36 


422659 18 } 


43 


5-56 


97097c 


.80 


577723 


6-36 


4222^7 


17 


44 


549027 


5-56 


970922 


.«o 


573104 


6-36 


42lb«)) 


16 


45 


549060 


5.55 


970574 


8c 


573456 


6-35 


42i5i4 


i3 


46 


549-'393 


5.55 


970827 


.80 


5-3^67 


6-35 


421.33 


14 


47 


35oo2o 


5.54 


970779 


.80 


579248 


6-34 


42075s 


i3 


48 


560359 


5-54 


970731 1 


.80 


579029 


6-34 


420371 12 1 


49 


500692 


5.53 


970683 ■ 


• 80 


D50009 


6-34 


419991 


II 


5o 


55.024 


5-53 


970635 


.80 


58o3S9 


6-33 


419011 


10 


5i 


9-551356 


3-52 


9-970586 


.80 


9-580769 


6-33 


io-4io23i 
4i8«5i 


t 


53 


55i657 


5-52 


970533 


.80 


581149 


6-32 


53 


55k).8 


5-52 


970490 


• 80 


58i528 


6-32 


418472 


7 


54 


552349 


5-5i 


970442 1 


.80 


581907 


6-32 


418093 


6 


55 


5526ik) 


5-51 


970894 1 


.80 


5b2286 


6-3i 


4I77U 


5 


56 


553010 


5-50 


970345 1 


.81 


582665 


6-3i 


4.7335 


4 


57 


55iUi 


5-5o 


970297 


.81 


583043 


6-3o 


416957 


3 


58 


553670 


5-49 


970249 1 


.81 


583422 


6-3o 


416578 


2 


59 


554000 


5-49 


770200 1 


.81 


583doo 


6-29 


416200 


I 


66 


554329 


5.48 


97c 32 1 


.81 


584177 


6-29 


413823 







Cosine 


D. 


SLae 


D. 


COUUi:i?. 


D. 


Tang. 








(69 I 


)EGR 


EE3.) 









SINES AND TANGENTS. (21 DEGREES.) 



39 



M. 


Sine 


D, 


Cosine | 


D. 


Tang. 


D. 


Cotang. 


60 


o 


9.554329 

554658 


5-48 


9970152 


.81 


9-534177 


6.29 


10-415823 


I 


5 


48 


970103 


.81 


584555 


6 


It 


40445 


It 


3 


5549B7 


5 


47 


970055 


.81 


584932 


6 


4i5o68 


3 


55531 5 


5 


47 


970006 


.81 


585309 


6 


-28 


414691 


57 


4 


555643 


5 


46 


969907 


.81 


585686 


6 


27 


414314 


56 


5 


555971 


5 


46 


969909 


.81 


586062 


6 


27 


413938 


55 


6 


556299 


5 


45 


969860 


.81 


586439 


6 


27 


4i3o6i 


54 


I 


556626 


5 


45 


96981 1 


• 81 


586810 


6 


26 


4i3i85 


53 


556953 


5 


44 


969762 


.81 


587190 


6 


26 


412810 


52 


9 


557280 


5 


44 


9697*4 


.81 


587066 


6 


25 


412434 


5i 


lo 


557606 


5 


43 


969663 


.81 


587941 


6 


25 


412059 


5o 


II 


9.557932 


5 


43 


9 • 9696 1 6 


.82 


9-5883i6 


6 


25 


10-411684 


8 


12 


558258 


5 


43 


969567 1 


.82 


588691 


6 


24 


411309 


i3 


558583 


5 


42 


969518 


.82 


589066 


6 


24 


410934 


47 


14 


558go9 


5 


42 


969469 1 


.82 


589440 


6 


23 


410060 


46 


i5 


559234 


5 


41 


969420 1 


.82 


589814 


6 


23 


410186 


45 


i6 


559558 


5 


41 


969370 


.82 


590188 


6 


23 


409812 


44 


\l 


559883 


5 


40 


969321 


.82 


590562 


6 


22 


409438 


43 


560207 


5 


40 


969272 


.82 


590935 


6 


22 


409065 
408692 


42 


19 


56o53i 


5 


39 


969223 


.82 


59i3o3 


6 


22 


41 


20 


56o855 


5 


39 


969173 


.82 


591681 


6 


21 


408319 


40 


21 


9.561178 


5 


38 


9-969124 


.82 


9-592054 


6 


21 


10-407946 


It 


22 


56i5oi 


5 


38 


969075 


.82 


592426 


6 


20 


407074 


23 


561824 


5 


37 


969025 
968976 


.82 


592798 


6 


20 


407202 


37 


24 


562146 


5 


ll 


.82 


593170 


6 


19 


406S29 


36 


25 


562468 


5 


968926 


.83 


593542 


6 


19 


406453 


35 


26 


562790 


5 


36 


968877 


.83 


593914 


6 


18 


406086 


34 


»^ 


563II2 


5 


36 


968827 


.83 


5942:35 


6 


18 


4057 1 5 


33 


563433 


5 


35 


968777 


.83 


594656 


6 


18 


405344 


32 


^9 


563755 


5 


35 


968723 


.83 


595027 


6 


17 


404973 


3i 


3o 


564075 


5 


34 


968678 


.83 


595398 


6 


n 


404602 


3o 


3i 


9.564396 


5 


34 


9.96S628 


.83 


9-595768 


6 


17 


10.404232 


ll 


32 


564716 


5 


33 


968578 


.83 


596133 


6 


16 


4o3862 


33 


565o36 


5 


33 


968528 


.83 


596508 


6 


16 


403492 


27 


34 


565356 


5 


32 


968479 


.83 


596878 


6 


16 


4o3i22 


26 


35 


565676 


5 


32 


96S429 


.83 


597247 


6 


i5 


402753 


25 


36 


565995 


5 


3i 


968379 


.83 


597616 


6 


i5 


402384 


24 


ll 


566314 


5 


3i 


968329 


• S3 


597985 


6 


i5 


4020 1 5 


23 


566632 


5 


3i 


96S278 


.83 


59^354 


6 


14 


401646 


22 


39 


566951 


5 


3o 


96S228 


• 84 


598722 


6 


14 


401278 


21 


40 


567269 


5 


3o 


968178 


.84 


599091 


6 


i3 


400909 


20 


41 


9-567587 


5 


29 


9-968128 


.84 


9-599459 


6 


i3 


10 -40054 1 


\l 


42 


567904 


5 


29 


968078 


.84 


099827 


6 


i3 


400173 


43 


56S222 


5 


28 


968027 


.84 


600194 


& 


12 


399806 


\l 


44 


56S539 


5 


28 


967977 


.84 


6oo562 


6 


12 


399438 


45 


568856 


5 


28 


967927 


.84 


600929 


6 


11 


399071 
398704 


ID 


46 


569172 


5 


27 


967^76 


.84 


601290 


6 


11 


:i 


ii 


569488 


5 


ll 


967826 


.84 


601662 


6 


II 


398338 


i3 


569 S04 


5 


967773 


.84 


602029 


6 


10 


397971 


12 


P 


570120 


5 


26 


967725 


.84 


602395 


6 


10 


397605 


II 


5o 


570435 


5 


25 


967674 


.84 


602761 


6 


10 


397239 


10 


5i 


9.570751 


5 


25 


9-967624 


.84 


9-6o3i27 


6 


09 


10-396873 


I 


52 


571066 


5 


24 


967573 


.84 


603493 


6 


09 


896507 


53 


57j38o 


5 


24 


967522 


.85 


6o3858 


6 


ll 


396142 


7 


?^ 


571695 


5 


23 


967471 


.85 


604223 


6 


390777 


6 


63 


572009 
572323 


5 


23 


967421 


.85 


604588 


6 


08 


_". ' ' ' 
390412 


5 


56 


5 


23 


967370 


• 85 


604953 
6o53i7 


6 


07 


390047 


4 


i^ 


572636 


5 


22 


967319 


.85 


6 


07 


394683 


3 


572950 


5 


22 


967268 


.85 


6o5682 


6 


07 


394318 


2 


^ 


D73263 


5 


21 


967217 


.85 


606046 


6 


06 


393904 


I 


(to 


573575 


5.21 


967166 


.85 


, 606410 


6.06 


393090 







Cosine 


D. 


Sine ' 


D. 


Cotiincr. 


._i^J 


Tu/ig. 



(68 DEGREES.li 



40 



(22 DB3^REES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 


1 





9.573575 


5.21 


9-967166 


85 


9-606410 


6.06 


10-393590 


60 


1 


573888 


5 


20 


9671 i5 


85 


606773 


6 


06 


392863 ! 5? 


2 


574200 


5 


20 


967064 


85 


607137 


6 


o5 


3 


574512 


5 


19 


967013 


85 


607500 


6 


o5 


3925^0 


57 


4 


574824 


5 


»9 


966961 


85 


607863 


6 


04 


392137 


56 


5 


575i36 


5 




966910 


85 


608225 


6 


04 


391775 


55 


6 


575447 


5 


18 


966859 
966808 


85 


6o8588 


6 


04 


391412 


54 


I 


575758 


5 


18 


85 


608950 


6 


o3 


391050 i 53 


576069 


5 


17 


966756 


86 


609312 


6 


o3 


390688 


52 


9 


576379 


5 


17 


966705 


86 


609674 


6 


o3 


3oo326 


5i 


10 


576689 


5 


16 


966653 


86 


6 10036 


6 


02 


3899O4 


5o 


II 


9-576999 
577309 


5 


16 


9-966602 


86 


9-610397 


6 


02 


10 389603 


ii 


12 


5 


16 


966550 


86 


610759 


6 


02 


389241 


i3 


577618 


5 


i5 


966499 


86 


611120 


6 


•01 


388880 


47 


H 


577927 


5 


i5 


966447 


86 


61 1480 


6 


•01 


388520 


46 


i5 


578236 


5 


14 


966395 


86 


611841 


6 


01 


388,59 


45 


i6 


578545 


5 


14 


966344 


86 


612201 


6 


• 00 


387799 


44 


17 


578853 


5 


i3 


966292 


86 


6i256i 


6 


-00 


387439 


43 


i8 


579162 


5 


i3 


966240 


86 


612921 


6 


•00 


387079 


42 


19 


579470 


5 


i3 


966188 


86 


613281 


5 


•99 


386719 


41 


20 


579777 


5 


12 


966136 


86 


6i364i 


5 


99 


386359 


40 


21 


9-58oo85 


5 


12 


9.966085 


87 


9-614000 


5 


98 


10^ 386000 


39 


22 


58o392 


5 


II 


966033 


87 


6i435o 
614718 


5 


98 


385641 


38 


23 


580699 


5 


II 


960981 


87 


5 


98 


385282 


37 


24 


58ioo5 


5 


II 


965928 


87 


61 5077 


5 


97 


3^4923 


36 


25 


58i3i2 


5 


10 


965876 


87 


6 1 5435 


5 


97 


384565 


35 


26 


58. 618 


5 


10 


965824 


87 


615793 


5 


97 


3S4207 


34 


27 


581924 


5 


09 


965772 


87 


6i6ni 


5 


96 


383849 


33 


28 


582229 


5 


09 


965720 


87 


6i65o9 


5 


96 


3S349I 


32 


29 


582535 


5 


09 


963668 


87 


616867 


5 


96 


3S3i33 


3i 


3o 


582840 


5 


08 


9656 1 5 


87 


617224 


5 


95 


3S2776 ' 3o 


3i 


9-583145 


5 


08 


9-965563 


87 


9-617582 


5 


95 


10.382418 


It 


32 


583449 


5 


07 


9655 11 


87 


617939 


5 


95 


382061 


33 


583754 


5 


07 


965458 


87 


618295 


5 


94 


38i7o5 


27 


34 


584058 


5 


06 


965406 


87 


61 8652 


5 


94 


381348 


26 


35 


584361 


5 


06 


965353 


88 


619008 


5 


94 


380992 


25 


36 


584665 


5 


06 


965301 


88 


619364 


5 


93 


38o636 


24 


ll 


584968 


5 


o5 


965248 


88 


619721 


5 


93 


3S0279 


23 


585272 


5 


o5 


960195 


88 


620076 


5 


93 


3-9924 


22 


39 


585574 


5 


04 


965143 


88 


620432 


5 


92 


379068 


21 


40 


585877 


5 


04 


965090 


88 


620787 


5 


92 


379213 


20 


41 


9-586179 


5 


o3 


9-965037 


88 


9.621142 


5 


92 


10.378858 


\l 


42 


586482 


5 


f)3 


964984 


88 


621497 


5 


91 


3785o3 


43 


586783 


5 


o3 


964931 


88 


621802 


5 


91 


378148 


17 


44 


587085 


5 


02 


964879 


88 


622207 


5 


90 


377793 


16 


45 


587386 


5 


02 


964826 


88 


622061 


5 


90 


377439 


i5 


46 


587688 


5 


01 


964773 


88 


622915 


5 


% 


377085 


14 


47 


587989 


5 


01 


964719 


88 


623269 


5 


376731 


i3 


48 


588289 


5 


01 


964666 


89 


623623 


5 


89 


376377 


12 


49 


588590 


5 


00 


964613 


89 


623976 


5 


89 


376024 


II 


5o 


588890 


5 


00 


964560 


89 


624330 


5 


88 


375670 1 10 1 


5i 


'ia 


4 


99 


9.964507 


89 


9.624683 


5 


88 


10-375317 


t 


52 


4 


99 


964454 


89 


620036 


5 


88 


374964 


53 


589789 
590088 


4 


99 


964400 


89 


625388 


5 


87 


374612 


7 


54 


4 


98 


964347 


89 


625741 


5 


87 


374209 


6 


55 


590387 


4 


9S 


064294 


89 


626093 


5 


87 


373907 


5 


56 


590.^86 


4 


97 


964240 


89 


626445 


5 


86 


3-3555 


4 


U 


5Q0984 


4 


97 


964187 


89 


' 626797 


5 


86 


373203 


3 


591282 


4 


97 


964133 


89 


627149 


5 


86 


372851 


2 


59 


591580 


4 


96 


964080 


89 


627501 


5 


85 


372499 
372148 


I 


66 


591878 


4-96 


964026 


89 


627852 


5 85 





Cosii e 


D. 


Sine 


D. 


Cotang. 


D. 


Tang. 1 M. | 



(67 DEGREES.) 



SINES AND TANGENTS. (23 EEGREES.) 



41 



M. 


Sine 1 


D. ! 


Cosine 


D. 1 


Tang. 


J). 


Cotang. 




o 


Q. 591878 


4.96 


9.964026 


.89 


9-627852 


5-85 


10-872148 


60 


1 


592176 


4.95 


968972 


.89 


628203 


5.85 


371797 


5? 


2 


592473 


4-95 


963919 


.89 


628554 


5-85 


371446 


3 


592770 


4-95 


968863 


.90 


628905 


5-84 


371095 


57 


4 


593067 


4.94 


968811 


<90 


629235 


5.84 


370745 56 


5 


5q3363 


4-94 


968757 


.90 


629606 


5-83 


370894 55 


6 


593559 


4-93 


968704 


.90 


629956 


5-83 


370044 54 


7 


593933 


4.93 


968650 


• 90 


680806 


5-83 


869694 53 


8 


594231 


4.93 


968596 


.90 


680656 


5-83 


360844 
368995 


52 


9 


594547 


4-92 


968542 


.90 


63ioo5 


5-82 


5i 


10 


594842 


4-92 


968488 


.90 


68i855 


5-82 


368645 


5o 


II 


9 595137 


4-91 


9.968434 


• 90 


9-681704 


5-82 


10-368296 


It 


12 


573432 


4-91 


968879 


.90 


682053 


5-81 


367947 


13 


593727 


4-91 


968823 


.90 


682401 


5-81 


367599 


47 


M 


596021 


4-90 


968271 


.90 


682730 


5-8i 


367230 


46 


i5 


5963 1 5 


4.90 


968217 


.90 


688098 


5-80 


366902 


45 


16 


llZt 


4-89 


968168 


.90 


688447 


5-8o 


366553 


44 


\l 


4-89 


963 1 08 


.91 


688795 


5-8o 


366205 


43 


597196 




968034 


.91 


684143 


5.79 


365857 


42 


19- 


597490 


4-88 


962999 


.91 


684490 


5-79 


365510 


41 


20 


5977^3 


4-88 


962945 


.91 


684888 


5-79 


365i62 


40 


21 


9.598075 


4-87 


9.962890 
962886 


•91 


9-635i85 


5.78 


io-3648i5 


It 


22 


59^368 


4-87 


.91 


635582 


5-78 


364468 


23 


598660 


4-87 


962781 


.91 


683879 


5-78 


364I2I 


37 


24 


598932 


4.86 


962727 


.91 


686226 


5-77 


868774 


36 


25 


599244 


4-86 


962672 


.91 


636572 


5-77 


368428 


35 


26 


599336 


4-85 


962617 


.91 


686919 


5-77 


363o8i 


34 


'^I 


599:^27 


4-85 


962362 


.91 


687263 


5-77 


362785 


33 


28 


600118 


4-85 


962308 


.91 


68761 1 


5.76 


362889 


32 


29 


600409 


4-84 


962438 


.91 


687936 


5.76 


362044 


3i 


3o 


600700 


4-84 


962898 


.92 


638302 


5-76 


361698 


3o 


3i 


9.600990 


4-84 


9.962843 


.92 


9-638647 


5.75 


10-361353 


11 


32 


601 2do 


4-83 


962288 


.92 


688992 


5-75 


361008 


33 


601370 


4-83 


962288 


.92 


689887 


5-75 


36o663 


27 


34 


601860 


4-82 


962178 


.92 


68968^ 


5-74 


36o3i8 


26 


35 


602 I 30 


4-82 


962128 


.92 


640027 


5-74 


359973 


25 


36 


602439 


4-82 


962067 


.92 


640871 


5-74 


359629 


24 


il 


602728 


4-8i 


962012 


.92 


640716 


5.73 


359284 
358940 


23 


38 


6o3oi7 


4.81 


961957 


.92 


641060 


5-73 


22 


39 


6o33o3 


4-8i 


961902 
961846 


.92 


641404 


5.73 


358596 


21 


4o 


603594 


4-8o 


.92 


641747 


5.72 


358253 


20 


41 


9.603882 


4-8o 


9.961791 


.92 


9-642091 


5-72 


10.357909 


19 


42 


604170 


4-79 


961785 


.92 


642484 


5-72 


337566 


18 


43 


604437 


4-79 


961680 


.92 


642777 


5-72 


337228 


n 


44 


604743 


4-79 
4-78 


961624 


.93 


648120 


5-71 


356880 


16 


45 


6o3o32 


961569 


.98 


648468 


5-71 


356^'» , iJ 1 


46 


6o53i9 


4-78 


9615.3 


.93 


648806 


5-71 


356104 


14 


47 


603606 


4-78 


96.438 


.93 


644148 


5.70 


355832 


i3 


48 


603892 


4-77 


961402 


.93 


644490 


5.70 


3555 10 


12 


49 


606179 


4-77 


961846 


•93 


644882 


5.70 


355i68 


li 


5o 


606465 


4-76 


961290 


•93 


645174 


5-69 


354826 


10 


5i 


9.606731 


4-76 


C-96I233 


.93 


9-643316 


5-69 


10-354484 


I 


52 


607036 


4-76 


961179 


.98 


643857 


5-69 


854143 


53 


607822 


4-75 


961.28 


•93 


646199 


5.69 


353801 


7 


54 


607607 


4-75 


961067 


.93 


64-'>340 


5-68 


353460 


6 


55 


607S92 


4-74 


96101 I 


•93 


646881 


5-68 


3331.9 

352778 


5 


56 


608.77 


4-74 


960933 


.98 


647222 


5.68 


4 


57 


608461 


4-74 


960899 


•93 


647362 


5.67 


352438 


3 


58 


60S745 


4-73 


960843 


.94 


647908 


5.67 


352097 


2 


h 


6ogo2g 


4-73 


960786 


.94 


648243 


5.67 


331737 


I 


6o 


609313 


4-73 


900780 


ij94_ 


648583 


5.66 


331417 







1 Co^.ne 


i D. 


Sine 


1 r. 


Cotaiisr. 


1 D. 


Tang. 


IT 



(66 DEGREES.) 



42 



(24 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Taug. 


D. 


Coiang. j 





9-6o93i3 


4-73 


9-960730 


94 


9-648583 


5-66 


>o-35i4i7 1 60 


I 


609397 


4 


72 


960674 


94 


648923 


5 


66 


351077 1 5o 

330737 1 sa 


3 


609880 


4 


72 


960618 


94 


649263 


5 


66 


3 


6 1 1 64 


4 


72 


96056 1 


94 


649602 


5 


66 


330398 57 


4 


610447 


4 


71 


96030: 


94 


649942 


5 


65 


330038 1 56 


5 


6S0729 


4 


71 


960448 


94 


6302 Si 


5 


65 


3497 '9 1 55 


6 


6 ! 1 ; 2 


4 


70 


960392 


94 


65o6ic 


5 


65 


349380 1 54 


7 


61 1294 


4 


70 


960335 


94 


630909 


5 


64 


349041 i 53 


8 


61 1076 


4 


in 


960279 


94 


65 1297 


5 


64 


348703 ' 52 


9 


6ii858 


4 


6q 


960222 


94 


63i6J6 


5 


64 


34S364 ' 5 1 


10 


612140 


4 


69 


960165 


94 


651974 


5 


63 


348026 


50 1 


II 


9-612421 


4 


69 


Q • 960 I 09 


95 


9-652312 


5 


63 


10-347688 


ii 


12 


612702 


4 


68 


96003 J 


93 


652630 


5 


63 


347330 


i3 


612983 


4 


68 


939995 


95 


652988 


5 


63 


347012 


47- 


14 


613264 


4 


67 


909933 


95 


653326 


5 


62 


346674 


46 


i5 


613545 


4 


67 


939S82 


95 


653663 


5 


62 


346337 


45 


)6 


6i3S25 


4 


67 


939S25 


95 


654000 


5 


62 


346000 


44 


»7 


6i4io5 


4 


66 


039768 


95 


654337 


5 


61 


343663 


43 


i8 


6i4385 


4 


66 


939711 


95 


654674 


5 


6i 


345326 


42 


J9 


614665 


4 


66 


939654 


95 


655011 


5 


61 


3449^9 


41 


20 


614944 


4 


65 


939396 


95 


655348 


5 


61 


344652 


40 


21 


9-6i5223 


4 


65 


9 •939339 


95 


9-655684 


5 


60 


io-3443i6 


^ 


22 


6i55o2 


4 


65 


939482 


95 


656020 


5 


60 


3439^0 


23 


615781 


4 


64 


939425 


95 


656356 


5 


60 


343644 


u 


24 


616060 


4 


64 


939368 


95 


636692 


5 


59 


343308 


25 


6 1 6338 


4 


64 


939310 


96 


657028 


5 


59 


3429^2 


35 


26 


616616 


4 


63 


939233 


96 


657364 


5 


59 


342636 


34 


27 


616894 


4 


63 


909195 


96 


657699 


5 


59 


342301 


33 


28 


617172 


4 


62 


939138 


96 


658o34 


5 


58 


341966 


32 


?9 


617450 


4 


62 


9390R1 


96 


658369 


5 


58 


34r63i 


3i 


So 


617727 


4 


62 


939023 


96 


658704 


5 


58 


341296 


3o 


3. 


9-618004 


4 


61 


9-958965 


96 


9-659039 
659373 


5 


58 


10-340961 


ll 


32 


018281 


4 


61 


93S908 


96 


5 


57 


340627 


33 


6i8558 


4 


61 


938850 


96 


659708 


5 


57 


340292 


ll 


34 


618834 


4 


60 


938792 


96 


660042 


5 


57 


339938 


35 


619110 


4 


60 


938734 


96 


660376 


5 


57 


339624 


25 


36 


619386 


4 


60 


938677 


96 


6607 1 


5 


56 


339290 


24 


ll 


619662 


4 


59 


958619 


96 


661043 


5 


56 


33S937 


23 


619938 


4 


59 


938561 


96 


661377 


5 


56 


33S623 


22 


39 


620213 


4 


ll 


9385o3 


97 


661710 


5 


55 


338290 


21 


40 


620488 


4 


958445 


97 


662043 


5 


55 


337957 


20 


41 


g-620763 


4 


58 


9-958387 


97 


9-662376 


5 


55 


10-337624 


\l 


42 


621038 


4 


57 


93S329 


97 


662709 


5 


54 


337291 


43 


62i3i3 


4 


57 


938271 


97 


663042 


5 


54 


336938 


n 


44 


621587 


4 


57 


9^8213 


97 


663375 


5 


34 


336625 


16 


4>> 


621861 


4 


56 


958134 


97 


663707 


5 


54 


336293 


i5 


46 


()22l35 


4 


56 


938006 


97 


664039 


5 


53 


333961 


14 


47 


622409 


4 


56 


938038 


97 


664371 


5 


53 


335629 


i3 


48 


622682 


4 


55 


937979 


97 


664703 


5 


53 


333297 


12 


49 


622956 


4 


55 


937921 
957863 


9^ 


665o35 


5 


53 


334965 


II 


5o 


623229 


4 


55 


97 


665366 


5 


52 


334634 


10 


5i 


9-623502 


4 


54 


9-937804 


97 


9-665697 


5 


52 


io-3343()3 


t 


52 


623774 


4 


54 


957746 


98 


666029 


5 


52 


333971 


53 


624047 


4 


54 


957687 


98 


666360 


5 


5i 


33364C 


7 


54 


624319 


4 


53 


937628 


98 


666691 


5 


5i 


333309 6 


55 


624591 


4 


a3 


957570 


98 


667021 


5 


5i 


332979 ' 5 


56 


624863 


4 


53 


937511 


98 


667352 


5 


5i 


332648 4 


57 


623135 


4 


32 


957432 


93 


667682 


5 


5o 


3323 1 8 - ■ 


3 


58 


625406 


4 


52 


957393 


98 


66801 3 


5 


5o 


331987 


1 


59 


625677 


4 


52 


957335 


9^ 


668343 


5 


5o 


33 1 657 


I 


6o 


623948 


4.31 


957276 


98 


668672 


5-5o 


33i328 





1 


Ckwino 


i D. 


Sine 1 


D. 


Cotanor. 


D- .. 


Tang. 


M. 



{Qo DEGREES.) 



SINES AND TANGENTS. (25 DEGREES.) 



la 






Sine } 
9-625948 1 


D. , 


CosillQ i 


D. 1 


Tansr. 


D. i 


Cotang. j 


4-5. 


9-937276 


.98 


9-668673 


5-50 


1 
io-33i327 60 


I 


626219 1 


4-5i 


9)7217 


.98 


669002 


5-49 


330Q98 59 
330668 58 


3 


626490 


4-5i 


957158 


.98 


669332 


5-49 


3 


6367^0 


4-50 1 


937099 


.98 


669661 


5.49 
5-48 


33o339 57 


4 


6y7o3o 


4-30 1 


937040 


.98 


66999, 


330009 55 


5 


627800 


4-00 i 


936981 


.98 


670320 


5-48 


329680 , 55 


6 


627570 


4-49 • 


9 '^ 69 2 1 


• 99 


670649 


5-48 


329351 


54 


7 


627840 


4-49 ! 


956S62 


•99 


670977 


5-48 


329023 


53 


8 


6.2S109 

628378 


4-49 1 


936803 


•99 


671306 


5-47 


32%94 


52 


9 


4-48 


906744 


•99 


671634 


5-47 


328366 


5i 


lo 


628647 


4-48 


936684 


•99 


67:963 


5.47 


328037 


5o 


(I 


9-628916 


4-47 


9.936625 


•99 


)-67229i 


5.47 


10-327709 


ii 


12 


629185 


4-47 [ 


Q 36 366 


•99 


672619 


5-46 


32738, 


i3 


629453 


4-47 , 


936306 


•99 


67 29 17 


5.46 


327053 


47 


14 


629721 


4.46 1 


956447 


•99 


673274 


5-46 


326726 


46 


i5 


629989 


4-46 


936387 


•99 


673602 


5.46 


326398 


45 


l6 


630237 


4.46 


956327 


•99 


673929 


5-45 


326071 


44 


17 


63o524 


4-46 


936268 


•99 


674237 


5.45 


325743 


43 


i8 


630792 


4-45 


936208 


I -00 


674584 


5.45 


325416 


42 


»9 


63 10^9 


4-45 


936148 


I -00 


674910 


5-44 


325090 


41 


20 


63i326 


4-45 


936089 


I -00 


675237 


5.44 


324763 


40 


21 


9-63i593 


4-44 


9-956029 


I- 00 


9-675564 


5-44 


10-324436 


U 


22 


631839 
632125 


4.44 


935969 


I -00 


675890 


5.44 


324110 


23 


4-44 


935909 


I -00 


676216 


5-43 


323784 


37 


24 


C32392 


4-43 


933849 


I -00 


676543 


5.43 


323457 


36 


25 


632658 


4-43 


955789 


I -00 


676S69 


5-43 


323i3i 


35 


26 


632923 


4-43 


955729 


I -00 


677194 


5-43 


322806 


34 


27 


633189 


4-42 


955669 


I-OO 


677520 


5.42 


322480 


33 


28 


633454 


4-42 


935609 
955548 


I -00 


677846 


5.42 


322154 


32 


29 


633719 


4-42 


I -00 


678171 


5.42 


321829 


3i 


3o 


633984 


4-41 


955488 


I -00 


678496 


5.42 


32i5o4 


3o 


3i 


9-634249 


4-41 


9.955428 


1 -01 


9.678821 


5-41 


10-321,79 


11 


32 


634514 


4.40 


955368 


I -01 


679146 


5.41 


320854 


33 


634778 


4-40 


955307 


I-OI 


679471 


5-41 


320529 
32o2o5 


27 


34 


635042 


4-40 


933247 


l-OI 


679795 


5.41 


26 


35 


6353o6 


4-39 


955186 


I-OI 


6S0120 


5-40 


319880 


25 


36 


635570 


4-39 


955126 


I-OI 


680444 


5-40 


319556 


24 


37 


635834 


4-39 


955o65 


I-OI 


680768 


5.40 


319232 


23 


38 


636097 


4-38 


955oo5 


I-OI 


681092 


5.40 


318908 


22 


39 


636360 


4-38 


954944 


I-OI 


681416 


5-39 


3 1 8584 


21 


40 


636623 


4-38 


954883 


I-OI 


681740 


5-39 


3i?26o 


20 


4i 


9-636886 


4-37 


9 954823 


I -01 


9.682063 


5.39 


10-3,7937 


\l 


42 


637148 


4-37 


934762 


I -01 


682387 


5-3o 
5-38 


317613 


43 


6374.1 


4-37 


954701 


I-OI 


682710 


317290 


\l 


44 


637673 


4-37 


954640 


I-OI 


683o33 


5-38 


316967 


45 


637935 


4-36 


9^4570 
934518 


I-Ol 


683356 


5-38 


316644 


i5 


46 


638197 
638458 


4-36 


1-02 


683679 


5-38 


3 16321 


U 


47 


4-36 


954457 


1-02 


684001 


5.37 


3,5999 


i3 


48 


1 638720 


4-35 


934396 


1-02 


684324 


5-37 


3 1 5676 


12 


49 


1 63Mg8i 


4-35 


934335 


1-02 


684646 


5.37 


3 15354 


II 


5o 


1 639242 


4.35 


954274 


1-02 


684968 


5-37 


3,5o32 


10 


5i 


9-6395o3 


4-34 


9-954213 


1-02 


9-685290 


5-36 


10-3,4710 


t 


52 


639764 


4-34 


954152 


1-02 


685612 


5-36 


3,4388 


53 


640024 


4-34 


954090 


1-02 


685934 


5-36 


3,4066 


I 


54 


640284 


4-33 


954029 

053968 


1-02 


686255 


5-36 


3,3745 


55 


640544 


4-33 


1-02 


686577 


5-35 


3,3423 


5 


56 


640804 


4-33 


5]?f5 


1-02 


686898 


5.35 


3,3,02 


4 


5-? 


641064 


4-32 


1-02 


687219 


5-35 


3,2781 


3 


68 


641324 


4-32 


933783 


1-02 


687540 


5.35 


312460 


2 


5g 


641584 


4-32 


933722 


i-o3 


^87861 


5-34 


3,2,39 
3,1818 


I 


6o 


641843 


4-3i 


953660 


I -03 


688182 


5.34 




M. 




Cosine 


D. 


1 Sine 


1 D. 


Cotan.of. 


D. 


Tans-. 








(61 


DEGR 


EES.^i 









44 



(26 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine E 


►. 


Tang. 


D. 


Cotang. 


1 
— 1 


o 


9-641842 


4-3i 


9-953660 I 


o3 


9-688182 


5.34 


io-3n8i8 


60 i 


I 


642101 


4 


3i 


953599 I 


o3 


688502 


5 


34 


311498 


U 


a 


642360 


4 


3i 


953537 I 


o3 


688823 


5 


34 


311177 


3 


642618 


4 


3o 


953475 I 


o3 


689143 


5 


33 


3 1 0857 


57 


4 


642877 


4 


3o 


953413 : 


o3 


689463 


5 


33 


3io537 


56 


5 


643 i35 


4 


3o 


953352 I 


o3 


689783 


5 


33 


310217 


55 


6 


643393 


4 


3o 


953290 I 


o3 


690103 


5 


33 


309897 


54 


7 


643650 


4 


29 


953228 1 


o3 


690423 


5 


33 


309577 


53 


8 


643908 


4 


29 


953166 I 


o3 


690742 


5 


32 


309258 
.08938 


52 


9 


644165 


4 


29 


953104 I 


o3 


691062 


5 


32 


5i 


ic 


644423 


4 


28 


953042 I 


o3 


691381 


5 


32 


308619 


5o 


II 


9.6446S0 


4 


28 


9-952980 I 


04 


9-691700 


5 


3i 


i3-3o83oo 


ii 


12 


6449-36 


4 


28 


952918 I 


04 


692019 
692338 


5 


3i 


307981 


i3 


64Mc3 


4 


27 


952855 I 


04 


5 


3i 


307662 


47 


14 


6i:)/,;)o 




27 


932793 I 


04 


692656 


5 


3i 


307344 


46 


i5 


645706 


4 


27 


932731 I 


04 


692975 


5 


3i 


307025 


45 


i6 


64S962 


4 


26 


932669 I 


04 


693293 


5 


3o 


306707 


44 


>7 


646218 


4 


26 


932606 I 


04 


693612 


5 


3o 


3o6388 


43 


i8 


646474 


'4 


26 


952544 I 


04 


693930 


5 


3o 


306070 


42 


»9 


646729 


4 


25 


952481 I 


04 


694248 


5 


3o 


3o5752 


41 


20 


646984 


4 


25 


952419 


04 


694566 


5 


29 


3o5434 


40 


21 


9-647240 


4 


25 


9-932356 I 


04 


9-694883 


5 


29 


io-3o5ii7 


ll 


23 


647494 


4 


24 


952394 I 


04 


693201 


5 


29 


304799 


23 


647749 


4 


24 


952231 I 


04 


6q55i8 


5 


29 


304482 


37 


24 


648004 


4 


24 


952168 I 


o5 


695836 


5 


29 
28 


304164 


36 


25 


648258 


4 


24 


952106 I 


o5 


696153 


5 


3o3847 


35 


26 


648512 


4 


23 


952043 I 


o5 


696470 


5 


28 


3o353o 


34 


27 


648766 


4 


23 


951980 I 


o5 


696787 


5 


28 


3o32i3 


33 


28 


649020 


4 


23 


951917 I 
95 1 854 I 


o5 


697103 


5 


28 


3o2'<97 
3o258o 


32 


?9 


649274 


4 


22 


o5 


697420 


5 


27 


3i 


3o 


649327 


4 


22 


951791 I 


o5 


697736 


5 


27 


302264 


3o 


3i 


9-649781 


4 


22 


9-951728 I 


o5 


9.69S053 


5 


27 


10.301947 


ll 


32 


65oo34 


4 


22 


95 1 665 I 


o5 


698369 


5 


27 


3oi63i 


33 


600287 


4 


21 


951602 I 


o5 


69H685 


5 


26 


3oi3i5 


27 


34 


65o539 


4 


21 


951539 I 


o5 


699001 


5 


26 


300999 


26 


35 


650792 


4 


21 


951476 I 


o5 


699316 


5 


26 


300684 


25 


36 


65 1 044 


4 


20 


951412 I 


o5 


699632 


5 


26 


3oo368 


24 


ll 


651297 


4 


20 


951349 I 


06 


699947 


5 


26 


3ooo53 


23 


65 1 549 


4 


20 


931286 I 


06 


700263 


5 


25 


299737 


22 


39 


65 1 800 


4 


•9 


951222 I 


06 


700578 


5 


25 


299422 


21 1 


40 


652032 


4 


19 


951159 I 


06 


700893 


5 


25 


299107 


20 


4i 


9-6523o4 


4 


;? 


9-951096 I 


06 


9-701208 


5 


24 


10.298792 


18 


42 


652555 


4 


95io32 I 


06 


701323 


5 


24 


29S477 


43 


652806 


4 


18 


930968 I 


06 


701837 


5 


24 


298163 


'7 


44 


653o57 


4 


18 


o5o9o5 I 
950841 I 


06 


702132 


5 


24 


297848 


16 


45 


6533o8 


4 


18 


06 


702466 


5 


24 


297534 


i5 


46 


653558 


4 


17 


950778 I 


06 


7027S0 


5 


23 


297220 


14 


% 


6538o8 


4 


17 


950714 I 


06 


703095 


5 


23 


29690.'. 


i3 


654059 


4 


n 


930650 . I 


06 


703409 


5 


23 


296391 


12 


49 


6543o9 


4 


16 


93o586 I 


06 


703723 


5 


23 


296277 


II 


5o 


654558 


4 


16 


95o522 I 


07 


704036 


5 


22 


295964 


10 


5i 


9 654808 


4 


16 


9-950458 I 


07 


9-704330 


5 


22 


10-293650 


i 


52 


655o58 


4 


16 


950394 I 


07 


704663 


5 


22 


293337 


53 


655307 


4 


i5 


93o33o I 


07 


704977 


5 


22 


293023 


7 


54 


655556 


4 


i5 


950266 I 


07 


705290 


5 


22 


2947 IP 


6 


55 


6558o5 


4 


i5 


930202 I 


07 


703603 


5 


21 


29439" 
294084 


5 


56 


656o54 


4 


t4 


9501 38 I 


07 


703916 


5 


21 


4 


57 


656302 


4 


14 


930074 I 


07 


706228 


5 


21 


293772 


3 


58 


656551 


4 


14 


950010 I 


07 


706541 


5 


21 


2Q3459 


2 


59 


656799 


4 


i3 


949945 I 


07 


706R54 


5 


21 


293146 


I 


66 


657047 


4-i3 


949881 I 


07 


707166 


5-20 


292834 




M. 


' Cosine 


1 D. 


Sine 1 I 


). 


Cotang. 


D. 


Tang. 



(63 DEGREES.) 



SINES AND TANGENTS. (27 DEGREES.) 



45 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




o 


9.657047 


4'i3 


9.949881 


1.07 


9.707166 


5.20 


10-292834 


60 


I 


657295 


4-i3 


949816 


1.07 


707478 


5.20 


292522 


59 


2 


607542 


4-12 


949732 


1-07 


707790 
708102 


5-20 


292210 


58 


3 


65779G 


4-12 


949688 


1-08 


5.20 


291898 


57 


4 


658o37 


4-12 


949623 


I -08 


708414 


5.19 


291386 


56 


5 


658284 


4-12 


949338 


1-08 


708726 


5.19 


291274 


53 


6 


658531 


4-II 


949494 


1.08 


709037 


5.19 


290963 


54 


? 


658778 


4-II 


949429 


I -08 


709349 


5.19 


290651 


53 


659025 


4-11 


949364 


1-08 


709660 


5.19 


290340 


32 


9 


659271 


4-10 


949300 


1-08 


709971 


5.18 


290029 


5i 


lo 


659517 


4-10 


949235 


1-08 


710282 


5.18 


289718 


5o 


n 


9.659763 


4-10 


9-949170 


1-08 


9.710593 


5.18 


10.289407 


it 


12 


660009 


4-09 


949103 


i-o8 


7 1 0904 


5.18 


^W 


i3 


660233 


4-09 


949040 
948975 


1.08 


711215 


5.18 


288783 


47 


14 


66o5oi 


4'OQ 


I -08 


711325 


5.17 


288475 


46 


i5 


660746 


4-09 


948910 

948845 


1.08 


711836 


5.17 


288164 


45 


i6 


660991 


4-o8 


1-08 


712146 


5.17 


287854 


44 


n 


661236 


4-o8 


948780 


1.09 


712436 


5.17 


287544 


43 


i8 


661481 


4-o8 


948713 


1.09 


712766 


5.16 


287234 


42 


19 


661726 


4-07 


948630 


1.09 


713076 


5.16 


286924 


41 


20 


661970 


4*07 


948584 


1.09 


713386 


5.16 


286614 


40 


21 


9.662214 


4-07 


9.948319 


1.09 


9.713696 


5.16 


io.2863o4 


It 


22 


662439 
662703 


4-07 


948454 


1-09 


7 1 4oo5 


5.16 


283995 


23 


4-o6 


948388 


1-09 


714314 


5.i5 


285686 


37 


24 


662946 


4-o6 


948323 


1-09 


714624 


5.i5 


285376 


36 


25 


663190 


4-o6 


948257 


1.09 


714933 


5.i5 


283067 


35 


26 


663433 


4-o5 


948192 


1-09 


715242 


5.i5 


284738 


34 


!J 


663677 


4*o5 


948126 


1.09 


7i555i 


5.14 


284449 


33 


663920 


4-o5 


948060 


1-09 


7 1 5860 


5.14 


284140 


32 


29 


664163 


4-o5 


947995 


I-IO 


716168 


5.14 


283832 


3i 


3o 


664406 


4-04 


947929 


l-IO 


716477 


5.14 


283523 


3o 


3i 


9.664648 


4-04 


9.947863 


1. 10 


9.716785 


5-14 


IO-2832I5 


29 


32 


664891 


4-04 


947797 


I-IO 


717093 


5.i3 


282907 1 28 1 


33 


665 1 33 


4-o3 


947731 


I-IO 


717401 


5.i3 


282399 


27 


34. 


665375 


4-o3 


047665 


l-IO 


717709 
718017 


5.i3 


282291 


26 


35 


665617 


4-o3 


947600 


l-lO 


5.i3 


281983 


25 


36 


665859 


4-02 


947333 


I-IO 


718325 


5.i3 


281670 


24 


ll 


666100 


4-02 


947467 


I-IO 


718633 


5.12 


281367 


23 


666342 


4-02 


947401- 


1. 10 


718940 


5.12 


281060 


22 


39 


■ 666583 


4-02 


947335 


I-IO 


719248 


5.12 


280732 


21 


40 


666824 


4-01 


947269 


I. 10 


719355 


5.12 


280445 


20 


41 


9.667065 


4*01 


9.947203 


I. 10 


9-719862 


5.12 


io.28oi38 


10 

18 


42 


667305 


4-01 


947136 


l-II 


720169 


5.11 


279831 


43 


667346 


4-01 


947070 


I. II 


720476 


5. 11 


27C-.24 


•7 


44 


667786 


4*00 


947004 


I. II 


720783 


5. II 


279217 


16 


45 


668027 


4-00 


946937 


I- 11 


721089 


5.11 


278911 


i5 


46 


668267 


4-00 


946871 


I . II 


721396 


5.11 


278604 


14 


47 


6685o6 


3.99 


946804 


I. II 


721702 


5.10 


278298 


i3 


48 


668746 


3-99 


946738 


I. II 


722009 
7223i5 


5.10 


277991 


12 


49 


668986 


3-99 


946671 


I-II 


5.10 


277683 


II 


50 


669225 


3.99 


946604 


I. II 


722621 


5.10 


277379 


JO 


5i 


9.669464 


3.98 


9-946538 


I. II 


9.722927 


5.10 


10-277073 


t 


52 


669703 


3.98 


946471 


I. II 


723232 


5.09 


276768 


53 


669942 


3.98 


946404 


I'll 


723538 


5.09 


276462 


7 


54 


670181 


3.97 


946337 


I- n 


723844 


5.09 


276i56 


6 


55 


670419 
670658 


3.97 


946270 


1-12 


724149 


5.09 


273831 


5 


56 


3-97 


946203 


1.12 


724434 


5.09 
5.08 


273346 


4 


ll 


670896 
671134 


3-97 


946 1 36 


I. 12 


724739 


275241 


3 


3.96 


946069 


I-I2 


723o65 


5.08 


274935 


3 


59 


671372 


3.96 


946002 


1-12 


725369 


5.08 


274631 


I 


66 


671609 


3.^6 


945935 


1-12 


725674 


5-08 


274326 





Cosine 


D. 


Sine 


D. 


Cotang. 


D. 


Tang. 


M. 



(62 DEGREES.) 



46 



(28 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 


60 


o 


9 67 1609 


3-96 


9.945935 


1. 12 


9.725674 


5 08 


ic. 274326 


I 


67i'S47 


3 


95 


943868 


1.12 


725979 


5 08 


274021 


U 


a 


6720S4 


3 


95 


945800 


I-I2 


726284 


5 


07 


273;i6 


3 


672321 


3 


95 


945733 


I-I2 


,26588 


5 


07 


273412 


u 


4 


672558 


3 


9: 


940666 


I-I2 


726892 


5 


07 


273io5 


5 


672795 
673o32 


3 


94 


945598 


1-12 


727197 


5 


07 


272S03 


55 


6 


3 


94 


945531 


I • 12 


727501 


5 


07 


272499 


54 


I 


673268 


3 


94 


945464 


I • l3 


727805 


5 


06 


272195 


'.i3 


673505 


3 


94 


945396 


1-13 


728109 


5 


06 


27.891 


32 


9 


673741 


3 


93 


945328 


I.i3 


728412 


5 


06 


27 . 588 


5i 


10 


6739- 


3 


93 


945261 


i.i3 


728716 


5 


06 


27.284 


50 


II 


9 674213 


3 


9? 


9-945193 


i-i3 


9-729020 


5 


06 


10-270980 


% 


12 


674448 


3 


92 


945i25 


i.i3 


729323 


5 


o5 


270677 


i3 


674684 


3 


92 


945o58 


1-13 


729626 


5 


o5 


270374 


47 


14 


674919 


3 


92 


944990 


i.i3 


729929 


5 


o5 


270071 


46 


i5 


675i55 


3 


92 


944^22 


i.|3 


730233 


5 


o5 


269167 


45 


i6 


675390 


3 


91 


944«54 


1-13 


73o535 


5 


o5 


269 ',65 


44 


17 


675624 


3 


91 


944786 


1-13 


73o838 


5 


04 


269162 


43 


18 


670859 


3 


91 


944718 


1-13 


731141 


5 


04 


268si59 


42 


19 


67601;/, 


3 


9' 


944650 


1-13 


731444 


5 


04 


268556 


41 


20 


676328 


3 


90 


944582 


1-14 


731746 


5 


04 


268254 


40 


2. 


9-676562 


3 


90 


9-944514 


I-I4 


9-732048 


5 


04 


10.267952 


39 


22 


676796 


3 


90 


044446 


1-14 


732351 


5 


o3 


267649 


38 


23 


677o3o 


3 


90 


944377 


1-14 


732653 


5 


o3 


267347 


u 


24 


677264 


3 


89 


944309 


I -14 


732955 


5 


o3 


267043 


25 


677498 


3 


89 


944241 


1.14 


733257 


5 


o3 


266743 


35 


26 


677731 


3 


89 


944172 


1-14 


733558 


5 


o3 


266442 


34 


11 


677964 


3 


88 


944104 


1.14 


733860 


5 


02 


266 1 40 


33 


678197 


3 


88 


944036 


I-I4 


734162 


5 


02 


265838 


32 


29 


678430 


3 


88 


943967 


1-14 


734463 


5 


02 


265537 


3i 


3o 


678663 


3 


88 


943899 


i-:4 


734764 


5 


02 


265236 


30 


3i 


9.678895 


3 


87 


9-043830 


1-14 


9-735o66 


5 


03 


10.264934 


It 


32 


679128 


3 


87 


94376. 


1-14 


735367 


5 


02 


264633 


33 


679360 


3 


87 


943693 


i-i5 


735668 


5 


01 


264332 


27 


34 


679392 


3 


87 


943624 


1-15 


735969 


5 


01 


s64o3i 


26 


35 


679^24 


3 


86 


943555 


I. .5 


736269 


5 


01 


263731 


25 


36 


68oo56 


3 


86 


9434B6 


i.i5 


736570 


5 


01 


263 i3o 


24 


37 


680288 


3 


86 


943417 


i-i5 


736871 


5 


01 


263 1 29 


23 


38 


68o5i9 


3 


85 


943348 


i-iS 


737171 


5 


00 


262^29 


22 


39 


680750 


3 


85 


943279 


I • i5 


737471 


5 


00 


262129 


21 


40 


680982 


3 


85 


943210 


i-i5 


737771 


5 


00 


262229 


20 


41 


o.68i2i3 


3 


85 


9-943i4t 


i-i5 


9-738071 


5 


00 


10-261929 


19 


42 


681443 


3 


84 


943072 


i-i5 


738371 


5 


00 


261629 


18 


43 


681674 


3 


84 


943oo3 


I- 15 


738671 


4 


99 


261329 


17 


44 


681905 


3 


84 


942934 


i-i5 


738971 


4 


99 


261029 


16 


45 


682135 


3 


84 


942^64 


i-n 


739271 


4 


99 


260729 


i5 


46 


682365 


3 


83 


942793 


I..6 


739570 


4 


99 


260430 


14 


47 


682095 


3 


83 


942726 


1-16 


739870 


4 


99 


260 1 3o 


i3 


48 


682825 


3 


83 


942656 


116 


740169 


4 


99 


25qS3i 


12 


49 


683o55 


3 


83 


942087 


1-16 


74046& 


4 


98 


209^32 


II 


5o 


683284 


3 


82 


942517 


1.16 


740767 


4 


98 


259233 


10 


5i 


9-683514 


3 


82 


9-942448 


i.;6 


9.741066 


4 


98 


10-258934 


t 


52 


683743 


3 


82 


942378 


i-i6 


741365 


4 


98 


25S635 


53 


683972 


3 


82 


9423o8 


1-16 


741664 


4 


98 


208336 


7 


5-4 


684201 


3 


8i 


942239 


i-i6 


741962 


4 


97 


258o38 


6 


5c 


684430 


3 


8i 


942169 


i-i6 


742261 


4 


97 


257739 


5 


56 


684658 


3 


81 


942099 


i-i6 


742509 


4 


97 


20-441 


4 


57 


684887 


3 


80 


942029 


i-i6 


74285:i 


4 


97 


207143 


3 


58 


685n5 


3 


80 


941909' 


i-i6 


743.06 


4 


97 


256844 


a 


59 


685343 


3 


So 


941889 


I-I7 


743454 


4 


97 


206546 


i 


60 


685571 


3.80 


941819 


1-17 


743752 


4.96 


206248 







CoBiue 


D. 


>-!ne 


D. 


Cotang. 


D. 


Tang. 



(61 DEGREES.) 



SINES AND TANGENTS. (29 DEGREES.) 



47 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


1 ^• 


Cotang. 1 


o 


9 685571 


3-8o 


9-941819 


1-17 


9-743752 


4-96 


io^a56a48 


60 


I 


685799 


3 


79 


941749 


117 


744o5o 


4.96 


255950 


u 


2 


686027 


3 


79 


941679 


I -17 


744348 


4.96 


255652 


3 


686254 


3 


79 


941609 


1-17 


744645 


4-96 


255355 


57 


4 


686iS2 


3 


]i 


941539 


1-17 


744943 


4.96 


255o57 


56 


5 


686709 


3 


941469 


1 -17 


745240 


4.96 


254760 


55 


6 


686936 


3 


78 


941398 


1-17 


745538 


4-9? 


214462 


54 


2 


687163 


3 


78 


941328 


1-17 


745835 


4-9= 


214165 53 1 


687389 


3 


78 


941258 


1-17 


746132 


4.91 


253868 


52 


9 


687616 


3 


77 


941187 


1-17 


746429 


4-95 


213571 


5i 


10 


687843 


3 


77 


941117 


1.17 


746726 


4-95 


253274 


5o 


II 


9-688069 


3 


77 


9-941046 


1..8 


9-747023 


4-94 


10 252977 


% 


12 


68H2Q5 


3 


77 


940975 


1.18 


747319 


4-94 


252681 


i3 


688.121 


3 


^6 


940905 


1-18 


747616 


4-94 


252384 


47 


14 


6S8747 


3 


76 


940834 


1-18 


747913 


4.94 


252087 


46 


i5 


68S972 


3 


76 


940763 


1-18 


748209 


4-94 


251791 


45 


i6 


6S9198 


3 


76 


940693 


1-18 


7485o5 


4.93 


211493 


44 


\l 


689423 


3 


75 


940622 


1-18 


748801 


4.93 


211199 


43 


6S9648 


3 


75 


94055 1 


i-i8 


749097 


4.93 


210Q03 


42 


19 


6^9^73 


3 


75 


9404^^0 


I -18 


749393 
749689 


4-93 


210607 


41 


20 


690098 


3 


75 


940409 


i-iS 


4.93 


25o3ii 


40 


21 


9-690323 


3 


74 


9-940338 


1-18 


9-749985 


4-93 


io-25ooi5 


39 


22 


690548 


3 


74 


940267 


i-i8 


750281 


4-92 


249719 38 1 


23 


690772 


3 


74 


940196 


1-18 


750176 


492 


249424 


37 


24 


690996 


3 


74 


940125 


1-19 


750872 


4-92 


249128 


36 


25 


691220 


3 


73 


940054 


1-19 


751167 


4-92 


24i^33 


35 


26 


691444 


3 


73 


939982 


1-19 


751462 


4-92 


248538 


34 


H 


691668 


3 


73 


939911 


1-19 


751757 


4-92 


248243 33 1 


28 


691S92 


3 


73 


939840 


1-19 


752012 


4-91 


2479 i« 


32 


^9 


692115 


3 


72 


93(p68 


1-19 


752347 


4-91 


247653 


3i 


3o 


692339 


3 


72 


939697 


1-19 


752642 


4-91 


247358 


3o 


3i 


9-692562 


3 


72 


9-939625 


1-19 


9-712937 


4-91 


10- 247063 


29 
28 


32 


692785 


3 


71 


939^54 


1-19 


753231 


4.91 


246769 


33 


693008 


3 


71 


939482 


1-19 


753126 


4-91 


246474 


11 


34 


693231 


3 


71 


939410 


1-19 


753820 


4.90 


246180 


35 


693453 


3 


71 


939339 


1-19 


754115 


4.90 


245885 


25 


36 


693676 


3 


70 


93926^ 


1-20 


754409 


4.90 


245591 


24 


11 


693 S98 


3 


70 


939195 


I -20 


754703 


4.90 


24''297 


23 


694120 


3 


70 


939123 


1-20 


754907 


4.90 


245oo3 


22 


39 


694342 


3 


70 


939012 


1-20 


755291 


4.90 


244709 


21 


40 


694564 


3 


69 


936980 


1-20 


755585 


4.89 


244413 


20 


41 


9-694786 


3 


69 


9.93S90S 


1-20 


9-755878 


4.89 


10-244122 


\t 


42 


693007 


3 


69 


93S836 


1-20 


756172 


4.89 


243828 


43 


695229 


3 


69 


938763 


1-20 


756465 


4.89 


243535 


17 


44 


695450 


3 


68 


938691 


1-20 


716719 


4-89 


243241 


16 


43 


695671 


3 


68 


938619 


I -20 


717012 


4.89 


2429 IS 


i5 


46 


695H92 


3 


68 


938547 


1-20 


757345 


4-88 


242655 


14 


% 


6961 i3 


3 


63 


938475 


1-20 


757638 


4-88 


242362 


i3 


690334 


3 


67 


938402 


1-21 


757931 


"^■fo 


242069 


12 


P 


690554 


3 


67 


93>^33o 


I-2I 


758224 


4-88 


241776 


II 


5o 


6967 7* 


7 


67 


938258 


I-2I 


758517 


4.88 


241483 


10 


5i 


9-696995 


3 


<57 


9 -93s 1 85 


I-2I 


9-758810 


4.88 


10-241190 


I 


53 


69-215 


3 


66 


9381.3 


1-21 


759102 


4-87 


240893 


53 


697435 


3 


66 


938040 


1-21 


759395 


4.87 


240605 


7 


54 


697654 


3 


66 


937967 


1-21 


719687 


4-87 


24o3i3 


6 


5f 


697874 


3 


66 


937^95 


1-21 


759979 


4-87 


24002 1 


5 


56 


69^094 


3 


•65 


937822 


1-21 


760272 


4-87 


239728 


4 


5^ 


6gS3i3 


3 


• 65 


9^7749 


1-21 


760164 


4-87 


239436 


3 


5fc 


6q8532 


3 


• 65 


937676 


1-21 


760856 


4-86 


239144 


2 


59 


698751 


3 


-65 


93-J604 


1-21 


761148 


4-86 


238852 


I 


6o 


698970 


3 


.64 


937531 


1-21 


761439 


4-86 


238561 







Cosine 


Ij 


X 


Sine 


D. 


Cotansr. 


D. 


Tamr. 


_^-.. 



27 



(60 DEGREES.) 



48 



(30 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine j 1>. 


T.ai-. 


D. 


Cotang. 







9.698970 


3.64 


9.937531 I 


21 


9-761489 


4.86 


10.238561 


60 


I 


699189 


3-64 


937458 I 


2i 


76I78I 


4-86 


288269 


It 


2 


699407 


3.64 


937385 I 


22 


762023 


4-86 


237977 


3 


699626 


3.64 


937312 I 


22 


762814 


4.86 


287686 


57 


4 


699844 


3-63 


987238 I 


22 


762606 


4.85 


137894 


56 


5 


700062 


3-63 


987165 I 


22 


762897 


4-85 


237103 


55 


6 


700280 


3-63 


987092 I 


22 


768188 


4-85 


286812 1 54 1 


7 


700498 


3.63 


987019 I 


22 


7684-9 


4.85 


236321 


53 


8 


700716 


3-63 


986946 I 
986872 I 


22 


768770 


4.85 


286280 


52 


9 


700933 


3-62 


22 


764061 


4.85 


283989 

235648 


5i 


10 


70ii5i 


3.62 


986799 I 


22 


764352 


4-84 


5o 


II 


9.701368 


3-62 


9.986725 I 


22 


9.764643 


4-84 


10.235357 


49 


12 


701585 


3-62 


986632 1 


23 


764933 


4.84 


285067 


48 


i3 


701802 


3.61 


986578 1 


23 


765224 


4.84 


284776 


47 


U 


7020T9 


3-6i 


9865o5 I 


23 


765514 


4-84 


284486 


46 


i5 


702236 


3.61 


986431 I 


23 


7658o5 


4-84 


284193 


45 


i6 


702452 


3.61 


986837 I 


23 


766095 


4-84 


288905 


44 


\l 


702669 


3-6o 


986284 I 


23 


766385 


4.88 


2836i5 


43 


702883 


3-60 


986210 I 


23 


766675 


4-83 


233823 


42 


'9 


7o3ioi 


3.60 


986186 1 


23 


766965 


4-83 


283o35 


41 


20 


703317 


3-6o 


986062 I 


23 


767255 


4-83 


282745 


40 


21 


9.703533 


3.59 


9.983988 1 


23 


9.767545 


4-83 


10.282455 


ll 


22 


703749 


3.59 


98 5^40 I 


23 


767884 
768124 


4-83 


282166 


23 


703964 


3.59 


23 


4.82 


281876 


37 


24 


704179 
•704395 


3.59 


983766 I 


24 


768413 


4.82 


23 1 587 


36 


25 


tu 


983692 I 


24 


768703 


4.82 


281297 


35 


26 


704610 


985618 I 


24 


»J 


4.82 


281008 


34 


27 


704825 


3.58 


935543 I 


24 


4-82 


280719 


33 


28 


700040 


3.58 


935469 I 


24 


769570 


4.82 


280480 


32 


29 


705254 


3-58 


935393 1 


24 


769860 


4.81 


280140 


3i 


3o 


705469 


3.57 


935320 I 


24 


770148 


4-8i 


22QS52 


3o 


3i 


9.705683 


3.57 


9-935246 1 


24 


9.770437 


4.81 


10.229563 


It 


32 


705898 


3.57 


985,71 I 


24 


770726 


4-81 


220274 
228985 


33 


706112 


3.57 


983097 I 


24 


771015 


4-81 


'I 


34 


706326 


3.56 


935022 I 


24 


77i3o3 


4-81 


228697 


26 


35 


706539 


3.56 


934948 I 


24 


771592 
771880 


4-81 


228408 


25 


36 


706753 


3-56 


984878 I 


24 


4.80 


228120 


24 


11 


706967 


3.56 


93479^ ^ 


25 


772168 


4.80 


227882 


23 


707180 


3.55 


984723 I 


25 


772457 


4-80 


227543 


22 


39 


707393 


3.55 


984649 I 


25 


772745 


4-80 


227255 


21 


40 


707606 


3.55 


934374 I 


25 


773o33 


4-8o 


226967 


20 


41 


9.707819 


3.55 


9-934499 I 


25 


9.773321 


4-80 


10.226679 


19 


42 


708032 


3.54 


934424 I 


25 


778608 


4-79 


226892 


18 


43 


708245 


3.54 


934849 I 


25 


773806 
774184 


4.79 


226104 


'I 


44 


708458 


3.54 


934274 1 


25 


4-79 


2258i6 


16 


45 


708670 


3-54 


934199 I 


25 


774.;] I 


4-79 


225329 


i5 


46 


708882 


3-53 


984128 1 


25 


774759 


4.79 


225241 


14 


47 


709094 


3.53 


984048 I 


25 


775046 


4-79 


224954 


i3 


48 


709806 


3.53 


988973 I 


25 


775333 


i]i 


224667 i 12 j 


49 


709518 


3.53 


988S98 1 


26 


775621 


224379 1 II 1 


5o 


709730 


3.53 


988822 I 


26 


775908 


4-78 


224092 


" 1 


5i 


9.709941 


3.52 


9.933747 I 


26 


9.776195 


4.78 


io.2238o5 


I 


52 


710153 


3.52 


988671 I 


26 


776482 


4.78 


2235i8 


53 


710364 


3.52 


933596 I 


26 


776769 


4.78 


228281 


I 


54 


710575 


3.52 


988520 1 


26 


777053 


4-78 


222943 


j 55 


710786 


3.5i 


983445 I 


26 


777342 


4-78 


222658 


5 ' 


56 


710997 
711208 


3.5i 


988869 I 
988293 I 


26 


777628 


4-77 


222872 


4 i 


ll 


3.5i 


26 


777915 


4-77 


222083 


3 


711419 


3.5i 


9882.7 I 


26 


778201 


4-77 


221799 


3 


59 


711629 


3.50 


988141 I 


26 


778487 


4-77 


22l5l2 


* 


60 


]iml 


3.50 


088066 1 


.26 


778774 


4-77 


221226 , j 




Cosine 


1 D. 


Sine 1 I 


). 


Cotansr. 


_2.-.__ 


___Tan2^ 


M. 1 



(59 DEGREES.) 



SINES AND TANGENTS. (31 DEGREES.) 



49 



M. 


Sine 


D. 1 


Cosine 


D. 1 


Tang. 1 


D. 


Cotang. 


60 





9-711839 


3.5o 


9.933066 


1-26 


9-778774 


4-77 


10.221226 


I 


7i2o5o 


3-50 


932990 


1-27 


779060 


4-77 


220940 


^5^ 


2 


712260 


3.5o 


932914 


1.27 


779346 


4-76 


220654 


3 


712469 


3-49 


932838 


1-27 


779632 


4-76 


2 20368 


57 


4 


712679 


3-49 


932762 


1-27 


779918 


4-76 


220082 


56 


5 


712889 
71J098 


3.49 


932685 


1-27 


780203 


4-76 


219797 


55 


6 


3-49 


932609 


1-27 


780489 


4-76 


219311 


54 


I 


7i33o8 


3-49 
3-48 


932533 


1-27 


780773 


4-76 


219225 


53 


7i35i7 


932457 


1-27 


781060 


4-76 


218940 


52 


9 


713726 


3.48 


932380 


1-27 


781346 


4-75 


218634 


5i 


ic 


713935 


3-48 


932304 


1-27 


781631 


4-75 


218369 


5o 


II 


9-714144 


3.48 


9.93'2228 


1.27 


9.781916 


4.75 


10-218084 


8 


13 


714352 


3.47 


93qi5i 


1-27 


782201 


4-75 


217799 


i3 


714361 


3.47 


932075 


1-28 


782486 


4-75 


217514 


47 


14 


714769 


3.47 


931998 


1-28 


782771 


4-75 


217229 


46 


i5 


7i497« 


3.47 


93 1 92 1 


1.28 


783o56 


4-75 


216944 


45 


i6 


7i5i86 


3.47 


931845 


1.28 


783341 


4-75 


216659 


44 


!^ 


715394 


3.46 


931768 


1-28 


783626 


4-74 


216374 


43 


7i56o2 


3-46 


931691 


1-28 


783gio 


4-74 


216090 


42 


»9 


713809 


3-46 


93.614 


1.28 


784195 


4-74 


2i58o5 


41 


20 


716017 


3.46 


931D37 


1-28 


784479 


4-74 


2l552I 


40 


21 


9-716224 


3-45 


9.931460 


1-28 


9-784764 


4-74 


io.2i5236 


U 


22 


716432 


3-45 


93 1 383 


1-28 


785048 


4-74 


214952 


23 


716639 


3-45 


93i3o6 


1.28 


785332 


4-73' 


214668 


11 


24 


716846 


3.45 


931229 


1.29 


7856i6 


4-73 


214384 


25 


717053 


3-45 


93 I 132 


1.29 


• 783900 


4-73 


214100 


35 


26 


717259 


3-44 


931075 


1.29 


786184 


4-73 


2i38i6 


34 


11 


717466 


3.44 


930998 


1-29 


786468 


4-73 


213532 


33 


717673 


3-44 


930921 


1-29 


786752 


4-73 


213248 


32 


?9 


717879 


3-44 


930843 


1-29 


787036 


4.73 


212964 


3i 


So 


718085 


3.43 


930766 


1.29 


787319 


4-72 


212681 


3o 


3i 


9-718291 


3.43 


9.930688 


1-29 


9.787603 


4-72 


10.212397 


11 


32 


718497 


3.43 


930611 


1.29 


787886 


4-72 


212114 


33 


718703 


3.43 


93o533 


r-29 


788170 


4-72 


2ii83o 


27 


34 


718909 


3.43 


93 0456 


1.29 


788453 


4-72 


211547 


26 


35 


719114 


3.42 


930378 


1-29 


788736 


4-72 


211264 


23 


36 


719320 


3-42 


93o3oo 


i-3o 


789019 


4-72 


210981 


24 


37 


719^25 


3.42 


930223 


i-3o 


789302 


4-71 


210698 


23 


38 


719730 


3-42 


930145 


1-30 


789585 


4-71 


2 1041 5 


22 


39 


719935 


3.41 


930067 


i-3o 


789868 


4-71 


210132 


21 


40 


720140 


3-41 


929989 


1-30 


79oi5i 


4-71 


209849 


20 


4i 


9-720345 


3-41 


9-92Q91I 


1.30 


9.790433 


4-71 


10.209567 


19 


42 


720549 


3.41 


929833 


1.30 


790716 


4-71 


209284 


10 


43 


720754 


3-40 


929755 


i.3o 


790999 


4-71 


209001 


^I 


44 


720958 


3-40 


929677 


1.30 


791281 


4-71 


208719 


16 


45 


721162 


3-40 


929399 


1-30 


791563 


4-70 


208437 


i5 


46 


721366 


3-40 


929521 


I -30 


791846 


4-70 


2081 54 


14 


47 


721570 


3-40 


929442 


1-30 


792128 


4-70 


207872 


i3 


48 


721774 


3.39 


929364 


1-31 


792410 


4-70 


207390 


13 


4o 


721978 


3.39 


1 929286 


1.31 


792692 


4-70 


207308 


II 


5o 


j 722181 


3.39 


929207 


1. 31 


792974 


4-70 


207026 


10 


5i 


i 9-722385 


3.39 


9-929129 


1-31 


9-793256 


4-70 


10-206744 


9 


52 


722588 


3-39 


929050 


1-31 


793538 


4-69 


206462 


8 


53 


722791 


3-38 


I -'3 1 


793819 


4-69 


206181 


I 


54 


722994 


3-38 


i-3i 


794101 


4-69 


205899 


55 


723197 


3-38 


928815 


i.3i 


794383 


4-69 


2o56i7 


' 5 


56 


723400 


3-38 


928736 


i-3i 


794664 


4-69 


205336 


4 


§ 


723603 


3-37 


928657 


1-31 


794945 


4-69 


2o5o55 


3 


7238o5 


3-37 


928578 


1-31 


795227 


4-69 
4-68 


204773 


2 


59 


724007 


3.37 


928499 


i.3i 


795508 


204492 


I 


6o 


724210 


3.37 


928420 


i.3i 


795789 


4-68 


204211 







Coeine 


D. 


Sine 


D. 


Cotan?. 


I D. 


>.Tan^- 


lir 



(58 DEGREES.) 



50 



(32 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Siuo 


D. 


Conine B. 


Tung. 


D. 


Cotani?. 


60 





9-724210 


3.37 


9-928420 I 


32 


9.795789 


• 4-68 


IO-20i2ll 


I 


724412 




37 


928342 I 


32 


796070 


4 


68 


2o393o 


5o 


2 


724614 




36 


928263 I 


32 


796351 


4 


68 


2o36',9 5S 1 


3 


724816 




36 


928183 I 


32 


796632 


4 


68 


203368 


57 


4 


723017 




36 


928104 1 


32 


796913 


4 


68 


2o3o^7 


56 


5 


720219 




36 


928025 I 


32 


797 « 94 


4 


68 


202S06 


55 


6 


725420 




35 


927946 I 


32 


79-7475 


4 


68 


2O2020 


54 


I 


720622 




35 


927867 I 


32 


797755 


4 


63 


202240 


53 


725823 




35 


927787 I 


32 


79S036 


4 


67 


2019^)4 


52 


9 


726024 




35 


927708 I 


32 


7yH3i6 


4 


67 


20 1 684 


5i 


lo 


726225 


3 


3o 


927629 1 


32 


798596 


4 


67 


201404 


5o 


II 


9.726426 


3 


34 


9-927549 I 


32 


9.798877 


4 


67 


10-201 123 


t 


12 


726626 


. 3 


34 


927470 1 


33 


799157 


4 


67 


200H43 


i3 


726827 


3 


34 


927390 I 


33 


799437 


4 


67 


200563 


47 


14 


727027 


3 


34 


927310 I 


33 


799717 


4 


67 


2002S3 


46 


i5 


727228 


3 


34 


927231 I 


33 


799997 


4 


66 


200003 


45 


i6 


727428 


3 


33 


927i5r I 


33 


800277 


4 


66 


199723 


44 


n 


727628 


3 


33 


927071 I 


33 


8oo507 


4 


66 


199443 


43 


i8 


727828 


3 


33 


926991 I 


33 


8oo836 


4 


66 


I9QI64 


42 


19 


728027 


3 


33 


92691 1 I 


33 


80M16 


4 


66 


I9S8S4 


41 


20 


728227 


3 


33 


926831 1 


33 


801396 


4 


66 


198604 


40 


21 


9-728427 


3 


32 


9-926751 I 


33 


9-801675 


4 


66 


10-108325 


39 


22 


728626 


3 


32 


926671 1 


33 


801905 


4 


66 


198045 


38 


23 


728825 


3 


32 


926591 I 


33 


802234 


4 


65 


197766 


37 


24 


729024 


3 


32 


926011 I 


34 


8o25i3 


4 


65 


197487 


36 


25 


729223 


3 


3i 


926431 I 


34 


802792 


4 


65 


197208 


35 


26 


729422 


3 


3i 


926351 I 


34 


803072 


4 


65 


196928 


34 


27 


729621 


3 


3t 


926270 I 


34 


8o335i 


4 


65 


196649 


33 


28 


729820 


3 


3i 


926190 I 


34 


8o363o 


4 


65 


1963-0 


32 


2g 


730018 


3 


3o 


926110 I 


34 


803908 


4 


65 


196092 


3 1 


3o 


730216 


3 


3o 


926029 I 


34 


804187 


4 


65 


195813 


3o 


3i 


9•^3o4I5 


3 


3o 


9-925949 1 


k 


9-804466 


4 


64 


10.195534 


It 


32 


7306 1 3 


3 


3o 




804745 


4 


64 


195255 


33 


7308 1 1 


3 


3o 


925788 I 


34 


8o5o23 


4 


64 


194977 


27 


34 


731009 


3 


29 


925707 I 


34 


8o53o2 


4 


64 


194698 


26 


35 


731206 


3 


29 


925626 I 


34 


8o5o8o 


4 


64 


194420 


25 


36 


73i4o4 


3 


29 


925545 I 


35 


8o5809 


4 


64 


194141 


24 


37 


731602 


3 


29 


923465 I 


35 


806137 


4 


64 


I93S63 


23 


38 


731799 


3 


29 
28 


925384 1 


35 


8064 1 5 


4 


63 


193585 


22 


39 


731996 


3 


9253o3 I 


35 


806693 


4 


63 


193307 


21 


40 


732193 


3 


28 


920222 1 


35 


806971 


4 


63 


193029 


20 


41 


9.732390 
732567 


3 


28 


9-925141 I 


35 


9.807249 


4 


63 


10-192751 


\l 


42 


3 


28 


920060 I 


35 


807527 


4 


63 


192473 


43 


732784 


3 


28 


924979 I 


35 


807805 


4 


63 


192195 


17 


44 


732980 


3 


27 


924897 1 


35 


808083 


4 


63 


191917 


16 


45 


733177 


3 


27 


924816 I 


35 


8o836i 


4 


63 


191639 


i5 


46 


733373 


3 


27 


924735 I 


36 


8o8638 


4 


62 


191362 


14 


47 


733569 


3 


27 


924604 I 


36 


808916 


4 


62 


1910S4 


i3 


48 


733760 


3 


27 


924572 1 


36 


809193 


4 


62 


190^07 


12 


49 


733961 


3 


26 


924491 I 


36 


809471 


4 


62 


190029 


II 


5o 


734107 


3 


26 


924409 I 


36 


809748 


4 


62 


190202 


10 


5i 


9.734353 


3 


26 


9-924328 I 


36 


9-810025 


4 


62 


10-189970 


t 


52 


734049 


3 


26 


924246 I 


36 


8io3o2 


4 


62 


189698 


53 


734744 


3 


25 


924164 I 


36 


8io58o 


4 


62 


189420 


1 


54 


734q39 


3 


25 


9240S3 I 


36 


810857 


4 


62 


189143 


6 


55 


735i3o 


3 


25 


924001 I 


36 


8iii34 


4 


61 


188866 


5 


56 


735330 


3 


25 


923919 I 


36 


811410 


4 


61 


i885qo 


4 


U 


735525 


3 


25 


923837 I 


36 


811687 


4 


61 


1 883 1 3 


3 


735719 


3 


•24 


923755 I 


37 


811964 


4 


61 


i88o36 


2 


59 


735914 


3.24 


923673 1 


37 


812241 


4 


61 


187759 




6o 


736109 


3-24 


923591 I 


37 


812517 


4-6i 


187483 







Cosine 


D. 


Sine 1 J). 


Cotang. 


D. 


Tang. 


M. 



(5*7 DEGREES.) 



SINES AND TANGENTS. (33 DEGREES.) 



51 



M. 




Sine 1 


D. 1 


Cosine D. 


Tang. 


D. 


Cotang. 


60 


"•?& 


3-24 


9-923591 I 


37 


9-8i25i7 


4-61 


10-187482 


I 


3- 


24 


923509 I 


37 


812794 


4 


6i 


187206 


It 


2 


736498 


3 


24 


923427 I 


37 


8i3o7o 


4 


61 


186930 


3 


736602 
736886 


3 


23 


923345 I 


37 


813347 


4 


60 


186653 


57 


4 


3 


23 


923263 I 


37 


8i3623 


4 


6c 


186377 


56 


5 


737080 


3 


23 


923181 I 


37 


813899 
814175 
814452 


4 


60 


186101 1 55 ! 


6 


737274 


3 


23 


923098 I 


37 


4 


60 


185825 


54 


I 


737467 


3 


23 


923016 I 


37 


4 


60 


185548 


53 


737661 


3 


22 


922933 I 

922851 I 


37 


814728 


4 


60 


185272 


52 


9 


737855 


3 


22 


37 


8i5oo4 


4 


60 


184996 


5i 


10 


738048 


3 


22 


922768 1 


38 


815279 


4 


60 


184721 


5o 


11 


9-738241 


3 


22 


9-922686 I 


38 


9-815555 


4 


59 


10-184445 


it 


12 


738434 


3 


22 


922603 I 


38 


8i583i 


4 


59 


184169 


i3 


738627 


8 


21 


922520 I 


38 


816107 


4 


59 


183893 


47 


14 


738820 


3 


21 


922438 I 


38 


8i6382 


4 


59 


i836i8 


46 


i5 


739013 


3 


21 


922355 I 


38 


8i6658 


4 


59 


183342 


45 


i6 


739206 


3 


21 


922272 I 


38 


816933 


4 


59 


183067 


44 


n 


739398 


3 


21 


922189 1 


38 


817209 


4 


59 


182791 


43 


i8 


739390 


3 


20 


922106 I 


38 


817484 


4 


59 


i825i6 


42 


19 


739783 


3 


20 


922023 I 


38 


817759 
818035 


4 


ll 


182241 


41 


20 


739975 


3 


20 


921940 I 


38 


4 


181965 


40 


21 


9-740167 


3 


20 


9-921857 I 


39 


9-8i83io 


4 


58 


10-181690 


39 


22 


740359 


3 


20 


921774 I 


39 


8i8585 


4 


58 


i8i4i5 


38 


23 


74o55o 


3 


19 


921691 1 


39 


818860 


4 


53 


181140 


37 


24 


740742 


3 


19 


921607 I 


39 


819135 


4 


58 


i8o865 


36 


25 


740934 


3 


19 


921524 I 


39 


819410 


4 


58 


180590 


35 


26 


74II25 


3 


19 


921441 I 


39 


819684 


4 


58 


i8o3i6 


34 


27 


74i3i6 


3 


\l 


921357 I 


39 


819959 


4 


58 


180041 


3J 


28 


741 5o8 


3 


921274 I 


39 


820234 


4 


58 


179766 


32 


29 


741699 


3 


18 


921190 I 


39 


82o5o8 


4 


57 


179492 


3i 


3o 


741889 


3 


18 


921107 I 


39 


820783 


4 


57 


179217 


3o 


3i 


9-742080 


3 


18 


9-921023 I 


39 


9-821057 


4 


57 


10-178043 


It 


32 


742271 


3 


18 


920039 I 


40 


821332 


4 


57 


178668 


33 


742462 


3 


n 


920856 I 


40 


821606 


4 


57 


178394 


27 


34 


742652 


3 


17 


920772 I 


40 


821880 


4 


57 


178120 


26 


35 


742842 


3 


17 


920688 I 


40 


822154 


4 


57 


177846 


25 


36 


743o33 


3 


17 


920604 I 


40 


822429 


4 


57 


177571 


24 


37 


743223 


3 


17 


920520 1 


40 


822703 


4 


57 


177297 


23 


38 


743413 


3 


16 


920436 I 


40 


822977 


4 


56 


177023 


22 


39 


743602 


3 


16 


920352 1 


40 


823250 


4 


56 


176750 


21 


40 


743792 


3 


16 


920268 I 


40 


823524 


4 


56 


176476 


20 


41 


9.743982 


3 


16 


9-920184 1 


40 


9-823798 


4 


56 


10-176202 


\t 


42 


744171 


3 


16 


920099 I 
920015 1 


40 


824072 


4 


56 


175928 


43 


744361 


3 


i5 


40 


824345 


4 


56 


175655 


\l 


44 


744550 


3 


i5 


919931 I 
919846 I 


41 


824619 
824893 


4 


56 


175381 


45 


744730 
744928 


3 


i5 


41 


4 


56 


175107 


i5 


46 


3 


i5 


919762 1 


41 


825166 


4 


56 


174834 


14 


^^ 


]%ll 


3 


i5 


919677 I 


41 


825439 
825713 


4 


55 


174561 


i3 


3 


14 


919593 I 


41 


4 


55 


174287 


12 


49 


745494 


3 


14 


919508 I 


41 


825986 


4 


55 . 


174014 


II 


5o 


745683 


3 


14 


919424 I 


41 


826259 


4 


55 


173741 


iO 


5i 


9-745871 


3 


14 


9-919339 I 


41 


9-826532 


4 


55 


10-173468 


t 


52 


746059 
746248 


3 


14 


919254 1 


41 


826805 


4 


55 


173195 


53 


3 


i3 


919169 I 


41 


827078 


4 


55 


172922 


I 


54 


746436 


4 


i3 


919085 I 


41 


827351 


4 


55 


172649 


55 


746624 


3 


i3 


919000 I 
918015 I 
918830 I 


41 


827624 


4 


55 


172376 


5 


56 


746812 


3 


i3 


42 


827897 


4 


54 


172103 


4 


57 


746999 
747187 


3 


.i3 


42 


828170 


4 


54 


171830 


3 


58 


3 


-12 


918745 I 


42 


828442 


4 


54 


171558 


2 


59 


747374 


3 


-12 


918659 I 


•42 


828715 


4 


54 


171285 


I 


60 


747562 


3-12 


918574 I 


-42 


828987 


4-54 


171013 







1 Cosine 


D. 


Sine I 


). 


Cotang. 


D. 


Tang. 


1l 



18 



(56 DEGREES.) 



52 



(3-t DEGREES.) A TABLE OF LOGARITHMIC 



["mT 


1 Sine 

1 


! ^' 


1 Cosine 


D. 


j Tang. 


I>. 


1 Cotang. 


i 


o 


9-74- '62 


, 3.12 


9-918574 


1-42 


9.828987 


4-54 


10-171013 


60 1 


I 


747749 


3.12 


918489 


1-42 


829260 


4-54 


170740 5q 
170468 58 


2 


747936 


3-12 


918404 


1-42 


829532 


4-54 


3 


748123 


3. II 


9i83i8 


1-42 


829805 


4-54 


170195 57 


4 


7483 10 


3-II 


918233 


1-42 


830077 


4-54 


169923 56 


5 


74^3683 


3.11 


918147 


1.42 


83o349 


4-53 


169651 55 


6 


3-11 


918062 


1-42 


83o62i 


4-53 


169379 54 


I 


748870 


3-11 


917976 


1-43 


830893 


4-53 


169107 53 


749056 


3.10 


917891 


1-43 


83ii63 


4-53 


168835 52 


9 


749243 


3-10 


917S05 


1-43 


831437 


4-53 


168563 5i 


xo 


749429 


3-ic 


917719 


1-43 


83i709 


4-53 


16S291 5o 


II 


9-749615 


3-10 


9-917634 


1-43 


9S^'98i 


4-53 


10-168019 4q 


12 


749801 


3-10 


917548 


1-43 


832253 


4-53 


167747 
167475 


48 


|3 


749987 


3.09 


917462 


1.43 


832525 


4-53 


47 


U 


750172 


3.09 


917376 


1.43 


832796 


4-53 


167204 


46 


ID 


730358 


3.0^ 


917290 


1-43 


833o68 


4-52 


166932 


, 45 


i6 


75o543 


3.09 


917204 


1.43 


833339 


4-52 


166661 


44 


\l 


750729 
730914 


i-S 


917118 
917032 


1-44 
1-44 


833611 
833882 


4-52 
4-52 


166389 
166118 


43 

42 


19 


701099 


3-08 


916946 


1-44 


834154 


4-52 


165846 


, 41 


20 


751284 


3-08 


916839 


1-44 


834425 


4-52 


165575 


40 


21 


9-751469 


3-o8 


'■& 


1-44 


9-834696 


4-52 


io-i653o4 


u 


22 


75i654 


3-08 


1-44 


834967 


4-52 


i65o33 


23 

24 


751839 
752023 


3-o8 
3.07 


916600 
9i65i4 


1-44 
1-44 


835238 

835509 


4-52 
4-52 


164762 
16449X 


37 

36 


23 


752208 


3.07 


916427 


1-44 


835780 


4-5i 


164220 


35 


26 


752392 


3.07 


916341 


1-44 


836o5i 


4-5i 


163949 
163678 


34 


27 


752576 


3-07 


916254 


1-44 


836322 


4-5i 


33 


28 


752760 


3.07 


916167 


1-45 


836593 


4-5i 


163407 


32 


29 


752944 


3-o6 


916081 


1-43 


836864 


4-5i 


i63i36 


3i 


3o 


753128 


3-06 


915994 


1.45 


837134 


4-5i 


162866 


3o 


3i 


9-753312 


3-06 


9.913907 
915820 


1-45 


9 -837405 


4-5i 


10-162595 


2I 


32 


753495 


3.06 


1-45 


837675 


4-5i 


162325 


33 


753679 


3-06 


915733 


1-45 


837946 


4-5i 


162054 


27 


34 


753862 


3-o5 


915646 


1-45 


838216 


4-5i 


161784 


26 


35 


754046 


3-05 


915339 


1-43 


838487 


4-5o 


i6i5i3 


25 


36 


754229 


3.o5 


915472 


1-45 


838737 


4-5o 


161243 


24 


37 


754412 


3-05 


91 5385 


1-45 


839027 


4-50 


160973 


23 


38 


754595 


3-e5 


915297 


1-45 


?^??I 


4-5o 


160703 


22 


39 


754778 


3-04 


9i52io 


1-43 


§^9363 


4.50 


160432 


21 


40 


754960 


3.04 


915123 


1.46 


339833 


4-5o 


160162 


20 


41 


9-755143 


3.04 


9-9i5o35 


1.46 


9-840108 


4-50 


10.159892 


It 


42 


755326 


3-04 


914948 
914860 


1-46 


840378 


4-50 


159622 


43 


755508 


3 -04 


1-46 


840647 


4-5o 


159353 


17 


44 


755690 


3-04 


914773 


1-46 


840917 


4-49 


J5^8?3 


16 


45 


755872 


3-03 


914685 


1.46 


841187 


4.49 


i5 


46 


756o54 


3-03 


914598 


1-46 


841457 


4.49 


158543 


14 


% 


756236 


3 -03 


914510 


1.46 


841726 


4.49 


158274 


i3 


756418 


3-o3 


914422 


1-46 


841996 


4.49 


i58oo4 


la 


49 


756600 


3-o3 


914334 


1-46 


842266 


4.49 


157734 


11 


5o 


756782 


3-02 


914246 


1-47 


842535 


4.49 


157465 


10 


5i 


9-756963 


3-02 


9-9i4i58 


1-47 


9 842805 


4-49 


10-157195 


t 


52 


757144 


3-02 


914070 


1-47 


843074 


4-49 


156926 


53 


757326 


3-02 


913982 
913894 


1-47 


843343 


4-49 


156657 


7 


54 


757507 


3-02 


1-47 


843612 


4.49 
4-43 


156388 1 


6 


55 


757688 


3-01 


913806 


1-47 


843882 


i56ii8 ■ 


5 


56 


757869 


3.01 


913718 


1-47 


844i5i 


4.48 


155849 i 


4 


y 


758o5o 


3-01 


9i363o 


1-47 


844420 


4-48 


155580 ; 3 


758230 


3-01 


913541 


1-47 


844680 
844958 


4.48 


i553ii 2 


59 


7584II 


3-01 


913453 


1-47 


4-43 


i55o42 i 


66 


753591 


3oi 


913365 


1-47 


845227 


4-43 


154773 




Cosine 


D. 


Sine 1 


D. 1 


Cotang. } 


D. 1 


Tang. < M. 








(55 


DSGRI 


:e8.^ 









SINES AND TANGENTS. (35 DEGREES.) 



53 



M, 


Siue 


D. 


Cosine I 


). 


Tang. 


D. 


Cotang. 


60 





9.758591 


3.01 


9.913365 1 


47 


9.845227 


4.48 


10.154773 


I 


758772 


3 


00 


918276 I 


47 


845496 


4.48 


1 54504 


It 


2 


758952 


3 


00 


918187 I 


48 


845764 


4.48 


154286 


3 


759132 


3 


00 


918099 I 


48 


846033 


4-48 


153967 
153698 


57 


4 


739312 


3 


00 


918010 I 


48 


846802 


4-48 


56 


5 


759492 


3 


00 


912922 1 


48 


846370 


4.47 


I 53480 


55 


6 


759672 


2 


99 


9I2S33 I 


48 


846889 


4-47 


i58i6i 


54 


I 


759852 


2 


99 


915=744 I 


48 


847107 


4-47 


152893 


53 


76003 1 


2 


99 


912655 I 


48 


847876 


4-47 


152624 


52 


9 


76021 1 


2 


99 


912566 I 


48 


847644 


4-47 


152856 


5i 


10 


760890 


2 


99 


912477 I 


48 


847913 


4-47 


152087 


5o 


II 


9-760569 


2 


98 


9-912888 I 


48 


9-848181 


4-47 


io.i5i8i9 


tl 


12 


760748 


2 


98 


912299 I 


49 


848449 


4-47 


i5i53i 


i3 


760927 


2 


98 


912210 I 


49 


848717 


4-47 


i5i283 


47 


14 


761 106 


2 


98 


912121 I 


49 


848986 


4-47 


i5ioi4 


46 


i5 


761285 


2 


k 


912081 I 


49 


849254 


4-47 


150746 


45 


i6 


761464 


2 


98 


91 1942 I 


49 


849322 


4-47 


150478 


44 


\l 


761642 


2 


97 


911858 I 


49 


849790 


4-46 


l5o2IO 


43 


761821 


2 


97 


911768 1 


49 


850038 


4-46 


149942 


42 


19 


761999 


2 


97 


911674 I 


49 


85o325 


4-46 


149673 


41 


20 


762177 


2 


97 


9II584 I 


49 


850598 


4-46 


149407 


40 


21 


9.762356 


2 


97 


9.911495 I 


49 


9 -850861 


4-46 


IO.I49I39 

I4887I 


u 


22 


762534 


2 


96 


911405 I 


49 


851129 


4-46 


23 


762712 


2 


96 


911815 I 


5o 


851896 


4.46 


148604 


3t 


24 


762889 


2 


96 


911226 I 


5o 


85i664 


4-46 


148386 


36 


25 


768067 


2 


96 


9iii36 I 


5o 


85iq3i 


4-46 


148069 


35 


26 


768245 


2 


96 


91 1046 I 


5o 


852i99 


4-46 


147801 


34 


27 


763422 


2 


96 


910906 I 


5o 


852466 


4.46 


147534 


33 


28 


763600 


2 


95 


910866 I 


5o 


852733 


4-45 


147267 


32 


29 


763777 


2 


95 


910776 I 


5o 


858001 


4-45 


146999 


3i 


3o 


768954 


2 


95 


910686 I 


5o 


858268 


4-45 


146782 


3o 


3i 


9.764181 


2 


95 


9-910596 I 


5o 


9-853585 


4-45 


10.146465 


11 


32 


764808 


2 


95 


9io5o6 I 


5o 


853802 


4-45 


146198 
145981 


33 


764485 


2 


94 


910415 I 


5o 


854069 
854386 


4-45 


27 


34 


764662 


2 


94 


910825 I 


5i 


4-45 


145664 


26 


35 


764888 


2 


94 


910285 I 


5i 


854608 


4-45 


145397 


25 


36 


765oi5 


2 


94 


910144 I 


5i 


854870 


4-45 


i45i3o 


24 


37 


765191 


2 


94 


910034 I 


5i 


855187 


4-45 


144863 


23 


38 


765367 


2 


94 


909968 I 


5i 


855404 


4-45 


144596 


22 


39 


765544 


2 


93 


909878 I 


5i 


855671 


4-44 


144329 


21 


4o 


765720 


2 


93 


909782 I 


5i 


855988 


4-44 


144062 


20 


4i 


9.765896 


2 


93 


9.909691 I 


5i 


9-856204 


4.44 


10- 148796 


\l 


42 


766072 


2 


93 


909601 I 


5i 


856471 


4-44 


143529 
143263 


43 


766247 


2 


93 


909510 I 


5i 


856737 


4-44 


17 


44 


766423 


2 


93 


'^u : 


5i 


857004 


4-44 


142996 
142730 


16 


45 


766598 


2 


92 


52 


837270 


4-44 


i5 


46 


766774 


2 


92 


909237 I 


52 


857587 


4-44 


142463 


14 


47 


766949 


2 


92 


909146 I 


52 


857803 


4-44 


142197 
141931 


i3 


48 


767124 


2 


92 


909055 I 
908964 I 
908878 I 


52 


838069 


4-44 


12 


49 


767800 


2 


92 


52 


858336 


4.44 


I4i664 


11 


5o 


767475 


2 


91 


52 


858602 


4-43 


141898 


10 


5i 


9.767649 


2 


91 


9-908781 I 
908690 1 


52 


9-858868 


4-43 


10.141182 


I 


52 


767824 


2 


91 


52 


859184 


4-43 


140866 


53 


767999 


2 


91 


908399 I 


52 


859400 


4-43 


140600 


7 


54 


768173 


2 


91 


908507 I 
908416 I 


52 


839666 


4-43 


140834 


6 


55 


768848 


2 


90 


53 


859982 


4-43 


140068 


5 


56 


768522 


2 


90 


908824 I 


53 


860198 


4-43 


189802 


4 


1 


768697 


2 


90 


908288 I 


53 


860464 


4-43 


189536 


3 


768S71 


2 


90 


908141 I 


53 


860780 


4-43 


189270 


2 


59 


769043 


2 


90 


908049 I 
907958 I 


53 


860995 


4-43 


I 39005 
18^739 


I 


60 


769219 


2-90 


53 


861261 


4-43 







Cosine 


D. 


Sine I 


). 


Cotan£f. 


D. 


Tang. 


^. 



(54 DEGREES.) 



51 



(36 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sino 


D, 


Cosine 


1 ^• 


Tang. 


1 D. 


Cotang. 




60 


o 


9-769219 


2-90 


9-907958 
907866 


1.53 


9-861261 


4-43 


io-i3873q 


I 


769393 


2 


.89 


1-53 


861 527 


4-43 


138473 


% 


2 


769566 


2 


89 


907774 


1-53 


861792 


4-42 


138208 


3 


769740 


2 


.89 


907682 


1-53 


8620D8 


4-42 


137942 


57 


A 


769913 


2 


.89 


907590 


1-53 


862323 


4-42 


137677 


56 


5 


770087 


2 


89 


907498 


1-53 


862589 


4-42 


137411 


55 


6 


770260 


2 


88 


907406 


1-53 


862854 


4-42 


137146 


54 


7 


770433 


2 


88 


907314 


1-54 


863! 19 


4-42 


13688 1 


53 


8 


770606 


2 


88 


907222 


1-54 


863383 


4-42 


i366i5 


52 


9 


770779 


2 


88 


907129 


1-54 


863650 


4-42 


136350 


5i 


10 


770952 


2 


88 


907037 


1-54 


863915 


4-42 


i36o85 


5o 


II 


9-771125 


2 


88 


9-906945 


1-54 


9.864180 


4-42 


10-135820 


% 


12 


771298 


2 


87 


906852 


1-54 


864445 


4-42 


135555 


l3 


771470 


2 


87 


906760 


1-54 


864710 


4-42 


135290 


47 


14 


771643 


2 


87 


906667 


1-54 


864975 


4-41 


135025 


46 


i5 


771815 


2 


87 


906575 


1-54 


865240 


4-41 


134760 


45 


i6 


771987 


2 


87 


906482 


1-54 


8655o5 


4-41 


134495 


44 


;? 


772159 


2 


87 


906389 


1-55 


865770 


4-41 


134230 


43 


772331 


2 


86 


906296 


1-55 


866o35 


4-41 


133965 


42 


19 


7725o3 


2 


86 


906204 


1-55 


866300 


4-41 


133700 


41 


20 


772675 


2 


86 


9061 1 1 


1-55 


866564 


4-41 


133436 


40 


21 


9-772847 
773018 


2 


86 


9-906018 


1-55 


9-866829 


4-41 


10-133171 


3^ 


22 


2 


86 


905925 


1-55 


867094 


4-41 


132906 


23 


773190 


2 


86 


905832 


1-55 


. 867358 


4-41 


132642 


V. 


24 


773361 


2 


85 


905739 


1-55 


867623 


4-41 


132377 


25 


773533 


2 


85 


905643 


1-55 


867887 


4-4i 


I32ii3 


35 


26 


773704 


2 


85 


905552 


1-55 


868i52 


4-40 


131848 


34 


27 


773875 


2 


85 


905439 


1-55 


868416 


4-4o 


I3i584 


33 


28 


774046 


2 


85 


905366 


1-56 


868680 


4-4o 


i3i32o 


32 


29 


774217 


2 


85 


905272 


1-56 


868945 


4.40 


i3io55 


3i 


3o 


774388 


2 


84 


9o5i79 


1-56 


869209 


4-40 


130794 


3o 


3i 


9-774558 


2 


84 


9 -905085 


1-56 


9-869473 


4.40 


io.i3o527 


29 


32 


774729 


2 


84 


904992 


1-56 


869737 


4.40 


i3o263 


28 


33 


774899 


2 


84 


904898 


1-56 


870001 


4.40 


12973? 


27 


34 


775070 


2 


84 


904804 


1-56 


870265 


4-40 


26 


33 


775240 


2 


84 


90471 1 


1-56 


870529 


4.40 


1 2947 1 


25 


36 


775410 


2 


83 


904617 


1-56 


870793 


4.40 


129207 


24 


V. 


775580 


2 


83 


904523. 


1-56 


871057 


4-40 


128943 


23 


775750 


2- 


83 


904429 


1-57 


871321 


4-40 


128679 
128415 


22 


39 


775920 


2- 


83 


904335 


1-57 


871585 


4-40 


21 


40 


776090 


2- 


83 


904341 


1-57 


871849 


4-39 


I28i5i 


20 


4i 


9-776259 


2 


83 


9-904147 


1-57 


9-872112 


4-39 


10-127888 


:i 


42 


776429 
77659S 


2 


82 


904053 


1-57 


872376 


4-39 


127624 


43 


2- 


82 


903959 


1-57 


872640 


4-39 


1273^10 


'7 


44 


776768 


2- 


82 


903864 


1-57 


872903 


4-39 


1270^17 


16 


45 


776937 


2- 


82 


903770 


1-57 


873167 


4-39 


126833 


i5 


46 


777106 


2- 


82 


903676 


1-57 


873430 


4-39 


126570 


14 


47 


777275 


2- 


81 


9o358i 


1-57 


873694 


4-39 


i263o6 


i3 


48 


777444 


2 


81 


903487 


1-57 
1-58 


873957 


4-39 


126043 


12 


49 


777613 


2 


81 


903392 


874220 


4-39 


125780 


II 


5o 


777781 


3 


81 


903298 


1-58 


874484 


4.39 


I255i6 


10 


5i 


9.777950 


2 


81 


9-9o32o3 


1-58 


9-874747 


4-39 


I0'i25253 


2 


52 


778119 


2- 


81 


903 1 08 


1-58 


875010 


4-39 


124990 


8 


53 


778287 


2 


80 


9o3oi4 


1-58 


875273 


4-38 


124727 


I 


54 


778455 


2 


80 


902919 


1-58 


875536 


4-38 


124464 


55 


778624 


2 


80 


902824 


1-58 


875800 


4-38 


124200 


5 


56 


778792 


2 


80 


902729 


1-58 


876063 


4-38 


133937 


4 


% 


778960 


2 


80 


902634 


1-58 


876326 


4-38 


123674 


3 


779128 


2 


80 


902539 


1-59 


876589 


4-38 


1 2341 1 


2 


59 


779295 


2 


^9 


902444 ■ 


1.59 


876851 


4-38 


I23i49 


1 


66 


779463 


2-79 


902349 


1-59 


877114 


4-38 


122886 







Cosine 


D. 


Sine 


D. 


Cotancr. 


D. 


Tang 



(53 DEGREES.) 



SINES ANT) TANGENTS. (37 DEGREES.) 



55 



M. 


Sine 


D. 


Cosiuo I 


). Tang. 


D. 


Cotang. 




o 


9-779463 


2-79 


9.902349 I 
902253 I 


59 


9-877114 


4-38 


10-122886 


60 


I 


779631 


2 


79 


^9 


877377 


4 


38 


122623 


u 


2 


779798 


2 


79' 


902158 1 


^9 


877640 


4 


38 


122860 


3 


779966 


2 


79 


902063 I 


^ 


877903 


4 


38 


\l]^l 


57 


4 


780133 


2 


?? 


901967 1 


59 


878165 


4 


38 


56 


5 


780300 


2 


901872 I 


59 


878428 


4 


38 


121572 


55 


6 


780467 


2 


"^^ 


901776 I 


^ 


878691 


4 


38 


121809 


54 


7 


780684 


2 


78 


901681 1 


59 


878953 


4 


37 


121047 


53 


8 


780801 


2 


78 


901585 I 


59 


879216 


4 


37 


120784 


52 


9 


780968 


2 


78 


901490 I 


59 


879478 


4 


37 


120522 


5i 


10 


781134 


2 


78 


901394 1 


60 


879741 


4 


37 


120259 


5o 


II 


9.781301 


2 


77 


9.901298 , I 


60 


9.880003 


4 


37 


10- 1 19997 


49 


12 


781468 


2 


77 ■ 


901202 I 


60 


880265 


4 


37 


119735 


48 


i3 


781634 


2 


77 


901 106 I 


60 


880528 


4 


37 


119472 


47 


14 


781800 


2 


77 


901010 I 


60 


880790 


4 


37 


119210 

II 8948 


46 


i5 


781966 


2 


77 


900914 I 


60 


88io52 


4 


37 


45 


i6 


782132 


2 


77 


C00818 I 


60 


881814 


4 


37 


1 1 8686 


44 


n 


782298 


2 


'^i 


900722 I 


60 


881576 


4 


37 


118424 


43 


i8 


782464 


2 


76 


900626 I 


60 


881889 


4 


37 


11B161 


42 


19 


782630 


2 


76 


900029 I 


60 


882101 


4 


37 


1 1 7899 


41 


20 


782796 


2 


76 


900433 I 


61 


882868 


4 


36 


117687 


40 


21 


9-782961 


2 


76 


9.900337 I 


61 


9.882625 


4 


36 


10-117375 


39 


22 


783,27 


2 


76 


900240 I 


61 


882887 


4 


36 


117118 


38 


23 


783292 
783458 


2 


75 


900144 I 


61 


888148 


4 


86 


116852 


37 


24 


2 


75 




61 


888410 


4 


36 


116590 


36 


25 


783623 


2 


'^i 


61 


888672 


4 


36 


116828 


35 


26 


783788 


2 


75 


61 


888984 


4 


36 


116066 


34 


27 


783953 


2 


7^ 


899757 I 


61 


884196 


4 


36 


ii58o4 


33 


28 


784118 




75 


899660 I 


61 


884457 


4 


36 


1x5543 


32 


H9 


784282 




74 


899564 I 


61 


884719 


4 


86 


ii528i 


3i 


v>o 


784447 




74 


899467 I 


62 


884980 


4 


36 


ll5020 


3o 


3i 


9.784612 


2 


74 


9.899370 I 


62 


9.885242 


4 


36 


10.114758 


20 

28 


32 


784776 


^ 


74 


899273 I 


62 


8855o3 


4 


36 


1 14285 


33 


784941 


2 


74 


899176 I 


62 


885765 


4 


86 


11 


34 


785io5 




74 


899078 I 


62 


886026 


4 


36 


113974 


35 


785069 




73 


898981 I 


62 


886288 


4 


36 


118712 


25 


36 


785433 




73 


898884 I 


62 


886549 


4 


35 


1x8451 


24 


3? 


785597 




73 


898787 I 


62 


886810 


4 


35 


1x8x90 


23 


38 


785761 




73 


898689 I 


62 


887072 


4 


35 


1x2928 


22 


39 


785925 




"7^ 


898592 I 


62 


887888 


4 


35 


1x2667 


21 


40 


786089 




73 


898494 I 


63 


887594 


4 


35 


1x2406 


20 


41 


9.786252 




72 


9.898397 I 


63 


9.887855 


4 


35 


10.112x45 


11 


42 


786416 




72 


898299 I 


63 


888116 


4 


85 


11x884 


43 


786579 




72 


898202 I 


63 


888377 


4 


85 


IXX623 


17 


44 


786742 


2 


72 


898104 I 


63 


888689 


4 


35 


ixx36i 


x6 


45 


786906 


2 


72 


898006 I 


63 


888900 


4 


85 


IXXIOO 


i5 


46 


''87069 


2 


72 


897908 I 


63 


889160 


4 


35 


1x0840 


14 


47 


787232 


2 


71 


897810 I 


63 


889421 


4 


35 


1x0579 


i3 


48 


787395 


2 


71 


■ 897712 I 


63 


889682 


4 


85 


110818 


12 


49 


787557 


2 


71 


897614 I 


68 


889943 


4 


35 


'1x0057 


XI 


5o 


787720 


2 


71 


897516 I 


63 


890204 


4 


34 


109796 


10 


5i 


9.787883 


2 


71 


9.897418 I 


64 


9.890465 


4 


34 


10- 109535 


I 


52 


788045 


2 


71 


897820 I 


64 


890725 


4 


34 


X09275 


53 


788208 




71 


897222 I 


64 


890986 


4 


34 


X 090 14 

108753 


7 


54 


788370 




70 


897123 1 


64 


891247 


4 


34 


6 


55 


788532 




70 


897025 1 


64 


891507 


4 


34 


108493 


5 


56 


788694 




70 


896926 I 


64 


891768 


4 


34 


108282 


4 


u 


788856 




70 


896828 I 


64 


892028 


4 


34 


107972 


3 


789018 




70 


896729 I 


64 


892289 


4 


34 


I077IX 


2 


59 


789180 




70 


896681 I 


64 


892549 


4 


34 


I0745X 




6o 


789342 




69 


896582 I 


64 


89281C 


4-34 


X07190 







Cosine 


"1 


). 


Sine i D. 


Cotaiig. 


D. 


. Tung. _ 


Jkj 



(52 DEGREES.) 



56 



(38 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine I 


). 


Tung. 


D. 


Ootang. 







9-789342 


2-69 


Q- 896532 I 


-64 


9-8928.0 


4-34 


10-107190 


60 


I 


789504 


2 


6q 


■ 896433 1 


-65 


898070 


4.34 


106980 


U 


2 


789665 


2 


69 


896335 1 


-65 


898881 


4.84 


106669 


3 


789827 
789988 


2 


69 


896286 1 


-65 


898091 
8988D1 


4.34 


106409 


57 


4 


2 


-69 


896187 1 


-65 


4.34 


106149 


56 


5 


790 '49 


2 


^? 


896088 I 


-65 


8941 11 


4.34 


105889 


55 


6 


7903 10 


2 


890089 I 
895840 1 


-65 


894871 


4.34 


105629 


54 


I 


790471 


2 


-68 


-65 


894632 


4-38 


10536? 1 53 1 


790632 


2 


-68 


893741 I 


-65 


894892 
895152 


4.33 


io5ioS 


52 


9 


790793 


2 


68 


895641 1 


-65 


4-38 


104848 


5i 


10 


790954 


2 


68 


895542 1 


.65 


895412 


4-33 


104588 


5o 


II 


9-791II5 


2 


68 


9-895443 1 


-66 


9-895672 


4-33 


10-104828 


1? 


12 


791275 


2 


67 


895343 I 


-66 


890982 


4-33 


104068 


i3 


791436 


2 


67 


895244 1 


-66 


896192 


4-38 


108808 


47 


14 


79i5o6 
79'757 


2 


67 


895145 1 


-66 


896452 


4-33 


103548 


46 


i5 


2 


67 


895045 1 


-66 


896712 


4-33 


108288 


45 


i6 


791917 


2 


67 


894945 I 


66 


896971 


4-33 


108029 


44 


n 


792077 


2 


67 


894846 1 


66 


897281 


4.33 


102769 


43 


i8 


•792237 


2 


66 


894746 1 


66 


897491 


4-83 


102009 


42 


19 


792397 


2 


66 


894646 1 


66 


897701 


4-33 


102249 


41 


20 


792557 


2 


66 


894546 1 


66 


898010 


4-38 


101990 


40 


21 


9-792716 


2 


66 


9-894446 I 


67 


9-898270 


4-38 


10-101730 


38 


22 


792876 


2 


66 


894846 1 


67 


898080 


4-33 


101470 


23 


793o35 


2 


66 


894246 1 


67 


898789 


4-38 


10.2.1 


37 


24 


793195 
793354 


2 


65 


894146 1 


67 


899049 
899808 


4-82 


10095. 


36 


25 


2 


65 


894046 1 


67 


4-32 . 


100692 
■ 100432 


35 


26 


79^514 


2 


65 


898046- 1 
898846 1 


67 


899568 


4.82 


34 


11 


798673 


2 


65 


67 


899827 


4-32 


100178 


33 


793832 


2 


65 


898745 1 


67 


900086 


4-82 


099914 


32 


29 


793991 
7941 5o 


2 


65 


898645 1 


67 


900846 


4-82 


099654 


3i 


3o 


2 


64 


893544 I 


67 


900605 


4-82 


099895 


3o 


3i 


9 -794308 


2 


64 


9-898444 I 


68 


9.900864 


4-32 


10-099186 


2Q 


32 


794467 


2 


64 


898848 1 


68 


90.124 


4-82 


098876 


28 


33 


794626 


2 


64 


898243 1 


68 


901888 


4-82 


098617 


27 


34 


794784 


2 


64 


898142 1 


68 


901642 


4-82 


098358 


26 


35 


794942 


2 


64 


898041 1 


68 


901901 


4-32 


098099 


25 


36 


795-01 


2 


64 


892940 I 


68 


902160 


4-82 


097840 


24 


37 


795259 


2 


63 


892889 1 


68 


902419 


4-32 


097581 


23 


38 


795417 


2 


63 


892789 1 


68 


902679 


4-82 


097821 


22 


39 


795575 


2 


63 


892688 1 


68 


902988 


4.82 


097062 


21 


40 


795733 


2 


63 


892536 I 


68 


908197 


4-3i 


096808 


20 


41 


9-795891 


2 


63 


9-892435 I 


69 


9.908455 


4-3i 


10-096545 


\l 


42 


796049 


2 


63 


892884 1 


69 


9087.4 


4-3i 


096286 


43 


796206 


2 


63 


892288 1 


69 


908978 


4.8. 


096027 


17 


44 


796864 


2 


62 


892182 1 


69 


904282 


4-3i 


090768 


16 


45 


790D2I 


2 


62 


892080 I 


69 


904491 


4-3i 


095009 


i5 


46 


796679 


2 


62 


891029 I 
80.827 I 
89S726 I 


69 


904750 


4-31 


095250 


14 


% 


796886 




62 


69 


900008 


4- 3 1 


094992 
094733 


i3 


796993 




62 


69 


900267 


4-3i 


12 


49 


797.5c 




61 


891624 1 


69 


900526 


4-3i 


094474 


11 


5o 


797807 




61 


89.528 1- 


70 


905784 


4-31 


094216 


10 


5i 


9.797464 




61 


9.891421 I- 


70 


9.906043 


4-31 


10.098957 


I 


52 


797621 




61 


891819 1 


70 


906302 


4-31 


098698 


53 


797777 




61 


891217 1- 


70 


9o656o 


4-3i 


098440 


7 


54 


797984 


2 


61 


8911.5 1- 


70 


906819 


4.3. 


098181 


6 


55 


798091 


2 


61 


89.0.3 1- 


70 


907077 


4-3i 


092928 


5 


56 


798247 


2 


61 


8909.1 1- 


70 


907886 


4-81 


092664 


4 


57 


798403 


2 


60. 


890809 I • 


70 


907594 


4-8i 


092406 


3 


58 


798060 


2 


60 


890707 1 - 


70 


907852 


4-3i 


092.48 


2 


59 


798716 


2 


60 


8qo6o5 1 - 


70 


9081.1 


4-3o 


091889 


1 


66 


798872 


2 


60 


89o5o3 1 - 


70 


908869 


4-3o 


091681 







Ooaine 


fj 


). 


Sine ]] 




Cotang. 


D. 


Tcxig. 1 :&L 1 



(51 DEGREES.) 



SINES AND TANGENTS. (39 DEGREES./ 



67 



M. 




Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




9.79S872 


2 -60 


9.890503 


1.70 


9.908369 
908628 


4-30 


10-091631 


60 


I 


799028 


2-6o 


890400 


1. 71 


4-30 


091372 


U 


2 


799184 


2 -60 


890'o8 


I-7I 


908886 


4-3o 


09 1 1 1 4 


3 


799339 
799495 


2.59 


8901^5 


1.71 


909144 


4-3o . 


090856 


57 


4 


2.59 


890093 


1. 71 


909402 


4-3o 


090598 


56 


5 


799631 


2.59 


889990 


1. 71 


909660 


4-3o 


090340 


55 


6 


799806 


2.59 


889888 


1-71 


909918 


4-3o 


090082 
089823 


54 


I 


799962 


2-59 


889785 


1-71 


910177 


4-3o 


53 


8001 17 


2.59 


889682 


1. 71 


910435 


4-3o 


089565 


52 


9 


800272 


2.58 


889579 


1.71 


910693 


4-3o 


089307 


5i 


10 


830427 


2-58 


889477 


1. 71 


910951 


4-3o 


089049 


5p 


II 


9.800582 


2-58 


9.889374 


1.72 


9.911209 


4-3o 


10.088791 


a 


12 


800737 


2.58 


889271 


1.72 


91 1467 


4-3o 


088533 


i3 


800892 


2-58 


889168 


1.72 


911724 


4-3o 


088276 


47 


14 


801047 


2-58 


88qo64 


1-72 


911982 


4-3o 


088018 


46 


i5 


801201 


2.58 


888961 


1.72 


912240 


4-3o 


087760 


45 


i6 


8oi356 


2.57 


888858 


1.72 


912498 


4-3o 


087502 


44 


n 


8oi5ii 


2.57 


888755 


1-72 


912756 


4-3o 


087244 


43 


i8 


80 1 665 


2.57 


888651 


1-72 


9i3oi4 


4-29 


086986 


42 


19 


801819 
801973 


2.57 


888548 


1.72 


913271 


4-29 


086729 


41 


20 


2.57 


888444 


1.73 


913529 


4-29 


086471 


40 


21 


g. 802128 


2.57 


9-888341 


1.73 


9.913787 


4-29 


10. 086213 


It 


22 


802282 


2.56 


888237 


1.73 


914044 


4-29 


085956 


23 


802436 


2.56 


888134 


1.73 


914302 


4-29 


085698 


37 


24 


802589 
802743 


2-56 


888o3o 


1.73 


914560 


4-29 


085440 


36 


25 


2.56 


887926 
887822 


1.73 


914817 


4-29 


o85i83 


35 


26 


802897 


2.56 


1.73 


915075 


4-29 


084925 


34 


^J 


8o3o5o 


2.56 


887718 


1.73 


915332 


4-29 


084668 


33 


803204 


2.56 


887614 


1.73 


915590 


4-29 


084410 


32 


?9 


803357 


2.55 


887510 


1.73 


915847 


4-29 


084153 


3i 


3o 


8o35u 


2-55 


887406 


1-74 


916104 


4-29 


083896 


3o 


3i 


9.803664 


2.55 


9.887302 


1-74 


9-916362 


4-29 


10.083638 


29 
28 


32 


803817 


2.55 


887198 


1-74 


916619 


4-29 


o8338i 


33 


803970 


2.55 


8870^3 


1-74 


916877 


4-29 


o83i23 


27 


34 


804123 


2.55 


1-74 


917134 


4-29 


082866 


26 


35 


804276 


2.54 


886885 


1-74 


917391 


4-29 


082609 


25 


36 


804428 


2.54 


886780 


1-74 


917648 


4-29 


082352 


24 


ll 


804381 


2.54 


886676 


1-74 


917903 


4-29 
4.28 


082095 


23 


804734 


2.54 


886571 


1-74 


918163 


081837 


22 


h 


804B86 


2.54 


886466 


1-74 


918420 


4-28 


o8i58o 


21 


4o 


8o5o39 


2.54 


886362 


1.75 


918677 


4.28 


o8i323 


20 


4i 


Q-8o5i9i 


2.54 


9.886257 


1.75 


9-918934 


4.28 


10-081066 


\l 


42 


805343 


2.53 


886 1 52 


1.75 


919191 


4.28 


080809 


43 


805495 


2.5S 


886047 


1.75 


919448 


4.28 


o8o552 


17 


44 


8o5647 


2.53 


885942 


1.75 


919705 


4.28 


080295 
o8oo38 


16 


45 


805799 


2-53 


885837 


1.75 


919962 


4-28 


i5 


46 


805951 


2.53 


885732 


1.75 


920219 


4.28 


079781 


14 


47 


806 I o3 


2.53 


885627 


1.75 


920476 


4-28 


079524 


i3 


48 


806254 


2.53 


885522 


1.75 


920733 


4-28 


079267 


12 


49 


806406 


2-52 


885416 


1.75 


920990 


4-28 


079010 
078753 


u 


5c 


806557 


2-52 


88531 1 


1.76 


921247 


4-28 


to 


5i 


9 806709 


2.52 


9-885205 


1.76 


9-921503 


4.28 


10-078497 


t 


52 


806860 


2.52 


885100 


1.76 


921760 


4.28 


078240 


53 


807011 


2.52 


884994 
884889 
884783 


1.76 


922017 


4-28 


077983 


■< 


54 


807163 


2-52 


1-76 


922274 


4.28 


077726 


6 


55 


807314 


2.52 


1-76 


922530 


4-28 


077470 


5 


l^ 


807465 


2.5l 


884677 


1.76 


922187 


4-28 


077213 


4 


ll 


807615 


2.5r 


884572 


1-76 


923044 


4-28 


076936 


. 3 


807766 


2.5l 


884466 


1.76 


923300 


4-28 


076700 


a 


h 


807917 


2.5l 


884360 


1.76 


923557 


4-27 


076443 


I 


60 


808067 


2.5i 


884254 


1.77 


9238i3 


4-27 


076187 







Cosine 


D. 


Sine 


D. 


Ootanfi:. 


D. ! 


Tang. 



(50 DEOiUCKS.) 



68 



(40 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


1 Cosine 


1 D. 


Tang, 


1 1^- 


CoUuig. 


60 





9-808067 


2-5l 


9.884254 


1-77 


9 -92381 3 


4-27 


10-076187 


I 


808218 


2-5l 


884148 


1-77 


924070 


4-27 


075980 


5o 


2 


8o8368 


2-5l 


884042 


1-77 


924327 


4-27 


075673 5§ 


3 


8oS5i9 


2-5o 


883936 


1-77 


92<i583 


4-27 


075417 5-7 
075160 56 


4 


808669 


2-50 


883.S29 


1-77 


924840 


4-27 


5 


808819 


2-50 


883723 


1-77 


920096 


4-27 


074904 55 


6 


808969 


2-5o 


883617 


1-77 


925352 


4-27 


074648 54 


7 


809119 


2 -50 


883510 


1-77 


925609 


4-27 


074891 53 


8 


809269 


2-5o 


883404 


.'•77 


925865 


4-27 


074185 52 


9 


809419 


2-49 


883297 


. 1-78 


926122 


4-27 


078878 


1 5i 


10 


809569 


2-49 


883191 


1-78 


926378 


4-27 


078622 


5o 


11 


9.809718 


2-49 


9-883084 


1-78 


9-926634 


4-27 


10-078866 


49 ' 


12 


809868 


2-49 


8S2977 


1.78 


926890 


4-27 


0781 10 


48 ' 


i3 


810017 


2-49 


882S71 


1.78 


927147 


4-27 


072853 


47 1 


U 


810167 


2-49 
2-48 


882764 


1.78 


927403 


4-27 


072597 


46 


i5 


8io3i6 


882657 


1-78 


927659 


4-27 


072841 


45 


i6 


810465 


2-48 


882550 


1-78 


927915 


4-27 


072085 


44 


\l 


810614 


2-48 


882443 


1-78 


928171 


4-27 


071829 


43 


810763 


2-48 


882336 


1-79 


928427 


4-27 


07 1 578 


42 


19 


810912 


2-48 


882229 


1-79 


928683 


4-27 


071817 


41 


20 


811061 


2-48 


882121 


1-79 


928940 


4-27 


071060 


40 


21 


9-811210 


2-48 


9-882014 


1-79 


9-929196 


4-27 


10-070804 


39 


22 


8ii358 


2-47 


881907 


1-79 


929452 


4-27 


070548 


38 


23 


8ii5o7 


2-47 


881799 


1-79 


92970S 


4-27 


070292 


V. 


24 


8ii655 


2-47 


881692 


1-79 


■ 929964 


4-26 


070086 


25 


811804 


2-47 


881 584 


1-79 


980220 


4-26 


069780' 


35 


26 


811952 


2-47 


88,477. 


1-79 


980475 


4-26 


069525 


34 


27 


812100 


2-47 


88.369 


1-79 


980781 


4 -.26 


069269 
069013 
068757 


33 


28 


812248 


2-47 


881261 


1-80 


980987 


4-26 


32 


29 


812896 


2-46 


8811 53 


1-80 


981248 


4-26 


3i 


3o 


812544 


2-46 


881046 


1-80 


981499 


4-26 


o685oi 


3o 


3i 


9-812692 


2-46 


9-880938 


1-80 


9-981755 


4-26 


10-068245 


29 
28 


32 


812840 


2-46 


88o83o 


I -80 


982010 


4-26 


067990 


33 


812988 


2-46 


880722 


1-80 


982266 


4-26 


067784 


27 


34 


8i3i35 


2.46 


880613 


I -So 


982522 


4-26 


067478 


26 


35 


8i3283 


2-46 


88o5o5 


I -80 


932778 


4-26 


067222 


25 


36 


8i343o 


2-45 


880397 


1-80 


983o33 


4.26 


066967 


24 


37 


813578 


2.45 


880289 


1-81 


988289 


4-26 


0667 1 1 


23 


38 


813725 


2-45 


880180 


1-81 


933543 


4-26 


066455 


22 


39 


813872 


2-45 


880072 


1-81 


988800 


4-26 


066200 


21 


40 


814019 


2-45 


879963 


1-81 


984056 


4-26 


065944 


20 


41 


9-814166 


2-45 


9-879855 


1-81 


9-984811 


4-26 


10-065689 
065433 


19 


'42 


8i43i3 


2-45 


879746 


1-81 


984567 


4.26 


ll 


43 


814460 


2-44 


879637 


1-81 


984823 


4-26 


o65i77 


17 


44 


814607 


2-44 


879529 


1-81 


985078 


4-26 


064922 


16 


45 


814753 


2-44 


879420 


1-81 


985333 


4-26 


064667 


i5 


46 


814900 


2-44 


8793 1 1 


1-81 


935589 


4-26 


06441 1 


14 


47 


81 5046 


2-44 


879202 


1-82 


935844 


4-26 


064 1 56 


i3 


48 


815193 


2-44 


879093 


1-82 


986100 


4-26 


068900 


12 ! 


49 


815339 


2-44 


878084 
878^75 


1-82 


936855 


4-26 


063645 


I 


5o 


8 15485 


2-43 


1-82 


986610 


4-26 


068890 


10 


5i 


9-815631 


2-43 


9-878766 


1-82 


9-986866 


4-25 


io-o63i34 


I 


52 


815778 


2-43 


878656 


1.82 


937121 


4-25 


062879 


53 


815924 


2-43 


878547 


1.82 


987876 


4-25 


062624 


7 


54 


816069 


2-43 


878438 


1-82 


987682 


4-25 


062868 


6 


55 


816215 


2-43 


878328 


1-82 


987887 


4-25 


062113 


5 


5e 


8i636i 


2-43 


878219 


1-83 


988142 


4-25 


061 858 


4 


U 


8i65o7 


2-42 


878109 


1-83 


988898 


4-25 


06160a 


3 


8x6652 


2.42 


877999 


1-83 


9386D3 


4-25 


061847 


2 


69 


816798 


2-42 


877890 


1-83 


988908 


4-25 


061092 I 
060837 ' 

Tang. 1 M. 


60 


816943 


2-42 


877780 


1-83 


989168 


4-25 




Cosine 


D. 1 


Sine ! 


D. 


Cotang. 


1 
J>. ! 


_... 






(49 


DEGRE 


ES.) 









SINES AND TANGENTS. (41 DEGREES.) 



59 



Mr 


Sine 


D. 


1 Cosiiie 


D. 


Taug. 


D. 


Cotaug. 


60 





0.816943 


2.42 


9.877780 


1 1-83 


9-989163 


4-25 


10-060887 


I 


817088 


2-42 


877670 


1 1-83 


989418 


4-25 


o6o582 


59 


2 


817233 


2-42 


877360 


1-83 


989673 


4-25 


060827 


58 


3 


817379 


2-42 


877430 


1-83 


989928 


4-25 


060072 


5? 


4 


817324 


2-41 


877340 


1-83 


940183 


4-25 


059S17 


56 


5 


817668 


2-41 


877230 


1-84 


940438 


4-25 


059062 


55 


6 


817813 


2-41 


877120 


1-84 


940694 


4-25 


059806 


54 


I 


817938 


:-4i 


877010 


1-84 


940949 


4-25 


009051 


53 


SiSinZ 


2-41 


876809 


1-84 


941204 


4-25 


058796 


52 


9 


1 Sj«247 


2-41 


876789 


1 1-84 


941458 


4-23 


058342 


5i 


10 


818392 


2-41 


876678 


1-84 


941714 


4-25 


058286 


5o 


II 


9.8i8536 


2.40 


9-876568 


1-84 


9-941968 


4-25 


io.o58o32 


49 


12 


818681 


2-40 


876457 


1.84 


942228 


4 25 


037777 


48 


i3 


818825 


2-40 


876847 


1-84 


942478 


4-25 


057522 


47 


i4 


818969 
819113 


2 -40 


876286 


. 1-85 


942733 


4-25 


007267 


46 


i5 


2.40 


876125 


1-85 


942988 


4-25 


057012 


43 


i6 


819237 


2-40 


876014 


1-85 


948243 


4-25 


006757 


44 


\l 


819401 


2-40 


873904 


1-85 


948498 


4-25 


006002 


43 


819545 


2-39 


875793 


1-85 


943732 


4-25 


056248 


42 


19 


819689 


2-39 


873682 


1-85 


944007 


4-25 


055998 
055788 


41 


20 


819832 


2-39 


873371 


1.85 


944262 


4-25 


40 


21 


9-819976 


2-39 


9-875439 
875348 


1.85 


9-944317 


4-25 


10-055483 


38 


22 


820120 


2-39 


1-85 


944771 


4-24 


000229 


23 


820263 


2.39 


875287 


1-85 


945026 


4-24 


004974 


37 


24 


820406 


2-39 


875126 


1.86 


943281 


4-24 


004719 


36 


23 


82o55o 


2-38 


875014 


1-86 


945535 


4-24 


054465 


35 , 


26 


820693 


2-33 


874903 


1.86 


945790 


4-24 


054210 


34 


11 


820836 


2-38 


874791 


1-86 


946045 


4-24 


053955 


33 


820979 


2-33 


874680 


1-86 


946299 


4-24 


053701 


32 


?9 


821122 


2-38 


874368 


1.86 


946554 


4-24 


053446 


3i 


3o 


821265 


2-33 


. 874436 


1.86 


946808 


4-24 


053192 


30 


3i 


9-821407 


2-33 


9-874344 


1-86 


9-947063 


4-24 


10.002987 


11 


32 


82i55o 


2-38 


874282 


1.87 


947818 


4-24 


052632 


33 


821693 
821835 


2.37 


874121 


1.87 


947372 


4-24 


052428 


11 


34 


2.37 


874009 


1-87 


947826 


4-24 


052174 


35 


821977 


2.37 


873896 


1-87 


948081 


4-24 


051919 


25 


36 


822120 


2-37 


873784 


1-87 


948336 


4-24 


o5i664 


24 


u 


822262 


2.37 


873672 


1.87 


948590 


4-24 


o5i4io 


23 


822404 


2.37 


873560 


1.87 


948844 


4-24 


o5iio6 


22 


39 


822346 


2.37 


873448 


1.87 


949099 


4-24 


000901 


21 


40 


822688 


2-36 


873335 


1-87 


949833 


4-24 


050647 


20 


41 


9.822830 


2-36 


9-873223 


1-87 


9-949607 


4-24 


10-000893 


\l 


42 


822972 


2-36 


878110 


1-88 


949862 


4-24 


o5oi38 


43 


823114 


2-36 


872998 


1.88 


9501 16 


4-24 


049884 


17 


44 


823255 


2-36 


8728S5 


1.88 


950870 


4-24 


049630 


16 


45 


823397 


2-36 


872772 


1.83 


950625 


4-24 


049875 


i5 


46 


823539 


2-36 


872659 


1.83 


950879 
95ii33 


4-24 


0491 21 


14 


47 
48 


823680 


2-35 


872547 


1-88 


4-24 


048867 


i3 


823821 


2-35 


872434 


1.83 


95 I 388 


4-24 


048612 


12 


49 


823963 


2-35 


872821 


1-83 


931642 


4-24 


043358 


II 


5(? 


824104 


2-35 


872208 


1.88 


951896 


4-24 


048104 


10 


5i 


0-824245 


2-35 


9.872095 


1.89 


9-932x50 


4-24 


10-047850 


Q 


52 


824386 


2-35 


?7'98i 


1-89 


952405 


4-24 


047395 


8 


53 


824327 
824668 


2-35 


871 803 


1.89 


952659 
952918 


4-24 


047341 


7 


54 


2-34 


871755 


1.89 


4-24 


047087 


6 


5c 


824808 


2-34 


871641 


1-89 


953167 


4-23 


046833 


5 


56 


824949 


2-34 


87.528 


1-89 


953421 


4-23 


046079 


4 


h 


825090 ! 


2-34 


871414 


1-89 


953675 


4-23 


046320 


3 


58 


82523c 


2-34 


871801 


1-89 


953929 
934183 1 


4-23 


046071 2 1 


^ 


825371 


2-34 


871187 


i-sl 


4-23 


045817 


I 


60 


8255II 


2-34 


871073 


1-90 


934437 ! 


4-23 


045563 







Cofiine 


D. 


Sine 


D. 


Cotang. 


D. 


Tanff. 


^ 








(48 


DEQUE 


KS.) 









(42 DEGREES.; A TABLE OF LOGARITHMIC 



M. 

o 


Sine 


D. 


Cosine I 


X 


Tung. 


D. 


Cotang. 1 


9.825511 


2-34 


9.871073 1 


.90 


9-954437 


4.28 


10 -045300 1 60 


I 


825651 


2 


.33 


870960 1 


.90 


954691 


4-23 


^ i U 


2 


823791 


2 


33 


870846 I 


-90 


954945 


4-23 


3 


825981 


2 


33 


870782 I 


-90 


955200 


4-23 


044800 


u 


4 


826071 


2 


33 


870618 I 


.90 


955454 


4-28 


044546 


5 


82621 1 


2 


33 


870504 1 


-90 


933707 


4-28 


044298 


55 


6 


826351 


2 


33 


870890 1 


-90 


953961 


4-23 


044089 


54 


7 


826491 
826631 


2 


83 


870276 1 


.90 


9562 1 5 


4-23 


048783 


53 


8 


2 


83 


870161 I 


.90 


956469 
956728 


4-28 


04853 1 


52 


9 


826770 


2 


82 


870047 1 


.91 


4-23 


048277 


5i 


ic 


826910 


2 


82 


869988 I 


-91 


956977 


4-23 


048028 


5o 


11 


9-827049 


2 


32 


9-869818 1 


91 


9.937231 


4-23 


10.042769 


t 


12 


827189 


2 


32 


8b97o4 1 


91 


957483 


4-23 


o425i5 


i3 


827328 


2 


32 


869389 I 


91 


937789 
937998 


4-23 


042261 


47 


14 


827467 


2 


82 


869474 I 


91 


4-23 


042007 


46 


i5 


827606 


2 


32 


869860 1 


91 


958246 


4-23 


041754 


45 


i6 


827745 


2 


32 


869245 1 


91 


958500 


4-28 


o4i5oo 


44 


17 


827884 


2 


81 


869180 I 


91 


958754 


4-28 


041246 


43 


i8 


828023 


2 


81 


869015 1 


92 


959008 


4-28 


040992 


42, 


»9 


828162 


2 


3i 


868900 I 


92 


939262 


4-23 


040788 


41 


20 


828301 


2 


3i 


868785 I 


92 


959516 


4-23 


040484 


40 


21 


9-828439 


2 


3i 


9-868670 I 


92 


9-959769 


4-23 


10-040281 


U 


22 


828578 


2 


81 


868555 I 


92 


960023 


4-28 


089977 


23 


828716 


2 


3i 


868440 I 


92 


960277 


4-^3 


089728 


37 


24 


828855 


2 


3o 


868824 I 


92 


96053 1 


4-23 


089469 


36 


25 


828993 


2 


3o 


868209 1 
868093 1 


92 


960784 


4-28 


089216 


35 


26 


829131 


2 


3o 


92 


961088 


4-23 


088962 


34 


27 


829269 


2 


3o 


867978 I 


93 


961291 


4-28 


088709 


33 


28 


829407 


2 


3o 


867862 I 


98 


961343 


4-23 


088453 


32 


29 


829545 


2 


3o 


867747 I 


93 


961799 


4-23 


088201 


3i 


So 


• 8296S3 


2 


3o 


867681 I 


93 


962032 


4-23 


087948 


3o 


3i 


9.829821 


2 


29 


9-867515 I 


93 


9-962806 


4-28 


10-087694 


It 


32 


829939 


2 


29 


867899 1 


93 


962360 


4-23 


087440 


33 


880097 


2 


29 


867283 I 


93 


962818 


4-23 


087187 


27 


34 


830234 


2 


29 


867,67 I 


93 


968067 


4-23 


086933 


26 


35 


83o372 


2 


29 


867031 I 


93 


968820 


4-23 


086680 


25 


36 


830309 


2 


29 


866935 I 
866819 I 


94 


968374 


4-23 


086426 


24 


37 


880646 


2 


29 


94 


968827 


4-23 


086178 


23 


38 


880784 


2 


29 


866708 I 


94 


964081 


4-23 


083919 


22 


39 


880921 


2 


28 


866586 I 


94 


964885 


4-23 


085665 


21 


40 


83io58 


2 


28 


866470 I 


94 


964588 


4-22 


o354i2 


20 


41 


9-88f io5 


2 


28 


9-866353 i 


94 


9-964842 


4-22 


io-o35i58 


\l 


42 


881882 


2- 


28 


866287 I 


94 


963095 


4-22 


o349o5 


43 


881469 


2 


28 


866120 I 


94 


963849 


4-22 


084651 


n 


44 


881606 


2 


28 


866004 1 


95 


963602 


4-22 


084898 


16 


45 


831742 


2 


28 


865887 I 


95 


965855 


4-22 


034145 


i5 


46 


881879 


2 


28 


865770 I 


95 


966103 


4-22 


088891 
088688 


14' 


47 


882013 


2 


27 


865653 I 


95 


966862 


4-22 


i3 


48 


832132 


2 


27 


865586 1 


95 


966616 


4-22 


038884 


12 


49 


882288 


2 


27 


863419 I 


95 


966869 


4-22 


o33i3i 


11 


5o 


832425 


2 


27 


865302 I 


95 


967123 


4-22 


082877 


10 


5i 


Q-88256I 


2 


27 


9-865185 I 


95 


9-967376 


4-22 


10-082624 


? 


52 


882697 


2 


27 


865o68 I 


95 


967629 


4-22 


082871 


53 


882888 


2 


27 


864950 I 


95 


967888 


4-22 


082117 


7 


54 


882969 


2 


26 


864883 I 


96 


968186 


4-22 


081864 


6 


55 


833103 


2 


26 


864716 I 


96 


968889 


4-22 


081611 


5 


56 


833241 


2 


26 


864598 I 
864481 I 


96 


968643 


4-22 


o3i357 


4 


11 


888877 


2 


26 


96 


068896 


4-22 


081104 


3 


833512 


2 


26 


864363 I 


96 


969149 


4-22 


o3o85i 


2 


09 


833648 


2 


26 


864245 I 


96 


969408 


4-22 


o8o5q7 ' 


I 


60 


833783 


2-26 


864127 I 


96 


969636 


4-22 


080844 







Cosine 


D. 


Sine r 


). 


Cotansr. 


D. 


Tauar. 1 


JsL^ 



(47 DEGREES.) 



SIXES -iND TANGEXT3. (43 DEaKEES.) 



61 



M. 




Siue 


D. 


Cosine 


D. 


Tang-. 


D. 


Cotang. 


60 


o 833783 


2.26 


9-864127 


1.96 


9.969656 


4-22 


io-o3o344 


I 


833919 


2-25 


864010 


1.96 


969909 


4-22 


030091 


^ 


2 


&34054 


2-25 


S63892 


1-97 


970162 


4-22 


029S38 


3 


834189 


2-25 


863774 


1-97 


970416 


4-22 


029584 


57 


4 


834323 


2-25 


863656 


1-97 


970669 


4.22 


029331 


56 


5 


834460 


2-25 


863538 


1-97 


970922 


4-22 


029078 


55 


6 


834595 


2-25 


863419 


1-97 


971175 


4-22 


028825 


54 


I 


834730 


2-25 


863301 


1-97 


971429 


4-22 


028571 


53 


834865 


2-23 


863 I 83 


1-97 


971082 


4.22 


o283i8 


52 


9 


834999 


2 24 


863o64 


1-97 


971935 


4-22 


028065 


5i 


10 


835134 


2-24 


862946 


1-98 


972188 


4-22 


0278x2 


5o 


II 


9-835269 
835403 


2-24 


9-862827 


1.98 


9-972441 


4-22 


10-027559 


it 


'^ 


2-24 


862709 


1.98 


972694 


4-22 


027306 


i3 


835538 


2-24 


. 862590 


1.98 


972948 


4-22 


02705.2 


47 


14 


835672 


2-24 


862471 


1.93 


973201 


4-22 


026799 


46 


ID 


835807 


2-24 


862353 


1.98 


973454 


4-22 


026546 


45 


i6 


835941 


2-24 


862234 


1.98 


973707 


4-22 


025293 


44 


I? 


836075 


2-23 


8621 1 5 


1.98 


973960 


4-22 


026040 


43 


i8 


836209 


2-23 


861996 


1-98 


9742x3 


4-22 


025787 


42 


19 


836343 


2-23 


861877 


1.98 


974466 


4-22 


025534 


41 


20 


836477 


2-23 


861758 


1.99 


974719 


4-22 


025281 


40 


21 


9 -83661 1 


2-23 


9-86i638 


1.99 


9.974973 


4.22 


10-025027 


3^ 


22 


836-45 


2-23 


86i5i9 


1-99 


975226 


4.22 


024-74 


23 


836S78 


2-23 


861400 


1.99 


975479 


4.22 


024521 


37 


24 


837012 


2-22 


861280 


1-99 


975732 


4-22 


024268 


36 


25 


837146 


2-22 


861161 


1-99 


975985 


4-22 


0240x5 


35 


26 


837279 
837ii^ 


2-22 


861041 


1-99 


976238 


4.22 


023762 


34 


H 


2-22 


860922 
860802 


1-99 


976491 


4.22 


>235o9 


33' 


28 


837546 


2-22 


1-99 


976744 


4-22 


023256 


32 


^9 


837679 


2-22 


860682 


2-00 


976997 


4-22 


023oo3 


3i 


So 


837812 


2-22 


86o562 


2-00 


977250 


4-22 


022750 


3o 


V 


9-837945 


2-22 


Q. 860442 


2-00 


9 -977503 


4-22 


10-022497 


29 


32 


838078 


2-21 


^ 86o322 


2-00 


977756 


4.22 


022244 


28 


33 


8382II 


2-21 


860202 


2-00 


978009 


4.22 


021991 


27 


34 


838344 


2-21 


860082 


2-00 


978262 


4.22 


021738 


26 


35 


838477 


2-21 


809062 


2-00 


9785x5 


4.22 


021485 


25 


36 


8386x0 


2-21 


859842 


2-00 


978768 


4-22 


021232 


H 


ll 


838742 


2-21 


859721 


2-01 


979021 


4-22 


020979 


23 


838875 


2-21 


859601 


2-01 


979274 


4-22 


020-26 


22 


39 


839007 


2-21 


859480 


2-01 


979527 


4-22 


020473 


21 


40 


839140 


2-20 


859360 


2-01 


979780 


4.22 


020220 


20 


41 


9-839272 


2-20 


9-859239 


2-01 


9 -930033 
^ 980286 


4.22 


10-019967 


]l 


42 


839404 


2-20 


8591 19 


2-01 


4.22 


OI9714 


43 


839536 


2-20 


85S998 


2-01 


980538 


4.22 


019462 


17 


44 


839668 


2-20 


858877 


2-01 


980791 


4.21 


0X9209 


16 


45 


839800 


2 -20 


858756 


2-02 


981044 


4.21 


0x8956 


i5 


46 


839932 


2-20 


858635 


2-02 


98 1 297 


4-21 


018703 


14 


47 


840064 


2-19 


8585i4 


2-02 


981550 


4.21 


018450 


i3 


48 


840196 


2.19 


858393 


2-02 


981803 


4.21 


OI8197 


12 


49 


840328 


2-19 


858272 


2-02 


9S2056 


4.21 


017944 


11 


5o 


840459 


2-19 


858i5i 


2-02 


982309 


4.21 


017691 


10 


5i 


9-840591 


2.19 


9-858029 
857908 


2-02 


9-982562 


4-21 


10-0X7438 


i 


52 


840722 


2-19 


2-02 


982814 


4-21 


017186 


53 


840854 


2-19 


857786 


2-02 


983067 


4-21 


016933 


7 


54 


840985 


2.19 


857665 


2-o3 


9S3320 


4-21 


016680 


6 


55 


841116 


2.18 


857543 


2-o3 


983573 


4-21 


0x6427 


5 


54 


841247 


2.18 


857422 


2-03 


983826 


4-21 


016174 


4 


ll 


841378 


2.18 


857300 


2.o3 


9840-9 


4.21 


015921 


3 


84 509 


2.18 


857178 


2-o3 


984331 


4-21 


0x5669 


2 


? 


84; 540 


2.18 


857056 


2-03 


984584 


4-21 


oi54i6 


I 


6o 


841771 


2.18 


856934 


2.o3 


984837 


4-21 


0i5i63 







Cosine 


D. 


Sine 


IX 


Cotan?. 


D. 


Taiigr. 


M. 



(46 DEGREES.) 



62 



(U DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


T;in,'. 


D. 


Cotang. 




o 


9-841771 


2.18 


9.856934 


2-03 


9-984837 


421 


io-oi5i63 


60 


I 


841902 


2.18 


856812 


2 


o3 


985090 


4 


21 


014910 


i? 


2 


842033 


2 


18 


856690 


2 


04 


985343 


4 


21 


014657 


3 


842163 


2 


n 


856568 


2 


04 


985596 


4 


21 


014404 


57 


4 


842294 


2 


17 


856446 


2 


04 


985848 


4 


21 


oi4i52 


56 


5 


842424 


2 


17 


856323 


2 


04 


9861.1 


4 


21 


013899 


55 


6 


842555 


2 


17 


850201 


2 


04 


986354 


4 


21 


013646 


54 


I 


842685 


2 


17 


856078 


2 


04 


986607 


4 


21 


013393 


53 


842815 


2 


17 


855956 


2 


04 


986860 


4 


21 


1 3 1 40 


52 


9 


842946 


2 


17 


855833 


2 


04 


987112 


4 


21 


0128S8 


5i 


10 


843076 


2 


n 


8557 1 1 


2 


o5 


987365 


4 


21 


012635 


5o 


II 


9-843206 


2 


16 


9-855588 


2 


o5 


9-987618 


4 


21 


IO-012382 


ii 


12 


843336 


2 


16 


855405 


2 


o5 


9S7871 


4 


21 


012129 


i3 


843466 


2 


16 


855342 


2 


o5 


988123 


4 


21 


011S77 


47 


14 


843595 


2 


16 


855219 


2 


o5 


9S8376 


4 


21 


01 1624 


46 


i5 


843725 


2 


16 


855096 


2 


o5 


988629 


4 


21 


0!l3-I 


45 


i6 


843855 


2 


16 


854973 


2 


o5 


9888^2 


4 


21 


OIII18 


44 


17 


843984 


2 


16 


854850 


2 


o5 


9^9134 


4 


21 


010866 


43 


18 


844114 


2 


i5 


854727 


2 


06 


9893S7 


4 


21 


oio6i3 


42 


19 


844243 


2 


i5 


834603 


2 


06 


989640 


4 


21 


oio36o 


41 


20 


844372 


2 


i5 


854480 


2 


06 


989893 


4 


21 


010107 


40 


21 


9-844502 


2 


i5 


9-854356 


2 


06 


9-990145 


4 


21 


10-009855 


It 


22 


844631 


2 


i5 


854233 


2 


06 


•990398 


4 


21 


009602 


23 


844760 


2 


i5 


854109 


2 


06 


99065 I 


4 


21 


009349 


37 


24 


844^89 


2 


i5 


853986 
853862 


2 


06 


990903 


4 


21 


009097 
008844 


36 


25 


845018 


2 


i5 


2 


06 


9911 56 


4 


21 


35 


26 


845147 


2 


i5 


853738 


2 


06 


991409 


4 


21 


oo85qi 


34 


27 


845276 


2 


14 


853614 


2 


07 


991662 


4 


21 


OOS338 


33 


23 


845405 


2 


14 


853490 


2 


07 


99'9«4 


4 


21 


0080S6 


32 


29 


845533 


2 


14 


853366 


2 


07 


992167 


4 


21 


007S33 


3i 


3o 


845662 


2 


14 


853242 


2 


07 


992420 


4 


21 


007580 


3o 


3i 


9-845790 


2 


14 


9-853ii8 


2 


07 


9.992672 


4 


21 


10-007328 


ll 


32 


845919 


2 


14 


852994 


2 


07 


992923 


4 


21 


00-075 


33 


846047 


2 


14 


852<'569 


2 


07 


993178 


4 


21 


006822 


27 


34 


846175 


2 


14 


852745 


2 


07 


993430 


4 




006070 


26 


35 


846304 


2 


14 


852620 


2 


07 


993683 


4 




oo63i7 


25 


36 


846432 


2 


i3 


852496 


2 


08 


993936 


4 




006064 


24 


ll 


846860 


2 


i3 


852371 


2 


08 


994189 


4 




oo58ii 


23 


846688 


2 


i3 


852247 


2 


08 


994441 


4 




005559 


22 


39 


846816 


2 


i3 


852122 


2 


08 


994694 


4 




oo53o6 


21 


4o 


846944 


2 


i3 


851997 


2 


08 


994947 


4 




oo5o53 


30 


41 


9.847071 


2 


i3 


9-85i872 


2 


08 


9.995199 


4 




10-004801 


\l 


42 


847199 


2 


i3 


851747 


2 


08 


995432 


4 




004548 


43 


847327 


2 


i3 


85i622 


2 


08 


995705 


4 




004295 


\l 


44 


847454 


2 


12 


851497 


2 


09 


995957 


4 




004043 


45 


847582 


2 


12 


85i372 


2 


09 


996210 


4 




003-90 


i5 


46 


847709 


2 


12 


851246 


2 


09 


996463 


4 




003537 


14 


47 


847836 


2 


12 


851121 


2 


09 


996715 


4 




oo328d 


i3 


48 


847964 


2 


12 


850996 


2 


09 


99.696S 


4 




oo3o32 


12 


49 


848091 


2 


12 


850870 


2 


09 


99-221 


4 




0027-9 


M 


5o 


848218 


2 


12 


850745 


2 


09 


997473 


4 




002027 


10 


5i 


9-848345 


2 


12 


9-85o6i9 


2 


09 


9.997726 


4 




IC- 002.274 


t 


52 


848472 


2 


II 


850493 


2 


10 


99-9-9 


4 




002021 


53 


848599 


2 


II 


85o36S 


2 


10 


99«23i 


4 




001769 


I 


54 


848726 


2 


II 


85o242 


2 


10 


99^^484 


4 


2 1 


001016 


55 


848852 


2 


II 


85oii6 


2 


IC 


,998737 


4 




001263 


5 


56 


848979 


2 


II 


849990 


2 


10 


99^^989 


4 




OOIOI I 


4 


,57 


849106 


2 


II 


849«64 


2 


10 


999242 


4 




000-08 


3 


58 


849232 


2 


II 


84973s 


2 


10 


999493 


4 




ooo5o5 


3 


59 


849359 


2 


II 


84961 1 


2 


10 


999-48 


4 


21 


000253 


I 


66 


849485 


2-II 


849485 


2- 10 


10- 000000 


4-21 


1 • 000000 





I Cosine 


D. 


Sine 


D. 


Cotancr. 


D. 


TalK^ 


JVL 



(45 DEGREES.) 



A TABLE OF NATURAL SINES. 



63 





Beg. 


1 Deg. 


2 Beg. 


3Deg. 


4 Deg. 


M 


M 


S. 


c.s. 


S. 


c. s. 


S. 


O.S. 


S. 


C.S. 


S. 


C.S. 


o 


00000 


Unit. 


01745 


99985 


08490 


99989 


o5234 


99868 


06976 


997 56 j 6a 


I 


00029 


I -0000 


01774 


99984 


o35i9 


9998H 


o5263 


99S61 


07005 


99734! 39 


2 


ooo58 


I '0000 


oi8o3 


99984 


08048 


99987 


05292 


99860 


07084 


99752 53 


3 


00087 


I. 0000 


01832 


99988 


03577 


99986 


o532i 


99858 


07068 


99750 57 


4 


001 16 


I -0000 


01862 


99988 


08606, 99935 


o535o 


99837 


07092 


99748 56 


5 


00145 


I -0000 


01891 


999^2 


03635 


99934 


05370 


99S55 


07121 


99746 55 


6 j 00175 


I -0000 


01920 


99982 


08664 


99933 


o54oc 


99834 


07i5o 


99744 54 


7 


00204 


1. 0000. 


01949 


99981 


08698 


99982 


05437 


99852 


07179 


99742 53 


8 


00233 


1. 0000 


01978 


99980 


037281 99981 


05466 


99851 


07208 


99740 52 


9 


00262 


1. 0000 


02007 


99980 


08752 


99980 


05495 


99849 


07237 


99738! 5i 


ID 


00291 


I .0000 


02036 


99979 


08781 


99929 


o5524 


99847 


j 07266 


99786} 5a 


II 


00320 


99999 


020651 99979 


o38io 


99927 


o5553 


99846 


07295 


99734 


it 


12 


00849 


99999 


02094 


99978 


08889 


99926 


o5582 


99844 


07824 


99731 


i3 


.00378 


99999 


02123 


99977 


08868 


99925 


o56ii 


99842 


07353 


99729 


47 


14 


00407 


99999 


02l52 


99977 


08897 


99924 


o564o 


99841 


07882 


9Q727 


46 


I? 


00436 


99999 


O2181 


99976 


08926 


99928 


05669 


99889 


0741 1 


99725 


45 


16 


00465 


99999 


022II 


99976 


08955 


99922 


05698 


99888 


07440 


99723 


44 


\l 


00495 


99999 


02240 


99973 


08984 


99921 


05727 


99886 


07469 
07498 


99721 


43 


00324 


99999 


02269 


99974 


0401 3 


99919 
99918 


o5756 


99834 


99719 


42 


19 


00553 


99998 


02298 


99974 


04042 


05785 


99833 


07527 


99716 


41 


20 


oo5S2 


99998 


02827 


99978 


04071 


99917 


o58i4 


99881 


07556 


99714 


40 


21 


0061 1 


99998 


02856 


99972 


04100 


99916 


05844 


99829 


07585 


99712 


ii 


22 


00640 


99998 


02885 


99972 


04129 


99915 


05873 


99827 


07614 


99710 


23 


00669 


99998 


02414 


99971 


04159 
04188 


99913 


C5902 


99826 


07643 


99708 


37 


24 


00698 


99998 


02443 


99970 


99912 


05981 


99824 


07672 


99705 


36 


25 


00727 


99997 


02472 


99969 


04217 


99911 


05960 


99822 


07701 


99708 


35 


26 


00756 


99997 


025oi 


99969 


04246 


99910 


05089 
06018 


99821 


07780 


99701 


34 


U 


00785 


99997 


02530 


99968 


04275 


99909 


99819 


07759 


99699 


33 


00814 


99997 


02560 


99967 


04804 


99907 


06047 


99817 


07788 


99696 


32. 


29 


00844 


99996 


02589 


99966 


04888 99906 


06076 


99815 


07817 


99694 


3i 


3o 


00873 


99996 


02618 


99966 1 


04862! 99905 


o6io5 


99S13 


07846 


99692 


3a 


3i 


00902 


99996 


02647 


99963 ! 


048911 99904 


06 1 34 


99812 


07875 


99689 


It 


32 


00981 


99996 


02676 


99964 j 


04420' 99902 


06168 


99810 


07904 


99687 


33 


00960 


99993 


02705 


99963 


04440 99901 


06192 


99808 


07988 


99685 


27 


34 


00989 


99995 


02784 


99968 


04478, 9990a 
04507 j 99898 


06221 


998061 


07962 


99683 


26. 


35 


01018 


99995 


02768 


99962 


o6?5o 


99804 


07991 


99680 


25 


36 


01047 


99995 


02792 


99961 


04536! 99897 


06279 
o63o8 


99808 


08020 


99678 


24 


37 


01076 


99994 


02821 


99960 j 


04365! 99896. 


99801 


08049 


99676 


23 


38 


oiio5 


99994 


o285o 


999391 


04594 99^94 


06887 


99799 


08078 


99673 


2i 


39 


01134 


99994 


02879 


99939! 


04628; 99898 


06366 


99797 


0S107 


99611 


21 


40 


01164 


99993 1 


02008 


99958 


04658! 99892 


06895 


99793 


081 36 


99668 


20 


41 


01193 


99993 


02988 


99937 


04682 99890 


06424 


99793 


o8i65 


99666 


J 9 


42 


01222 


99993 


02967 


999,-)6 


047 1 1 99880 
04740 99888} 


06453 


99792 


08194 


99664 


18 


43 


0125l 


99992 


02996 999551 


06482 


9979a 
99788 


08228 


99661 


17 


44 


O12S0 99992 


08025 


99934 


04769' 99886I 


o65ii 


08252 


99639 


16 


45 


oi3o9 99991 


o3o54 


99953 


0479B 


99885 


06540 


99786 


08281 


99657 


ID 


46 


01338 99991 


o3o83 


99932 1 


04827 


99883 


06569 
06598 


99784 


08810 


99654 


14 


^l 


01 367 99991 


03lI2 


99932 i 


04856 


99882! 


99782 


08339 


99632 


i3 


48 


01396 99990 


08141 


999311 


04885 99881 1 


06627 


997801 


08868 


99649 


12 


49 


01 423 99990 


08170 


99930 


04914' 998-79! 


06656! 99778 


0S897 


99647 


n 


5o 


OI404 999^9 


08190 99949' 


04948! 99878! 


o6685j 99776 


08426 


99644 


10 


5i 


014S3 


999S9 


03228 99948: 


04972 


99876 


06714, 99774 


08455 


99642 


1 


52 


oi5i3 


999H9 
99988 


08237 


99947 j 


o5ooi 


99873 


06748, 99772 


08484 


99539 


53 


01 542 


08286 


99946; 


o5o3o 


99873 


06773 


99770 


o85i8 


99687 


7 


54 


oi5ti 


99988 


08816 


99943 


o5o59 
o5o88 


99872 


06802 


99768 


08542 


99635 


6 


55 


01600 


99987 


03345 


99944 


99870 


06881 


09766 


08571 


99682 


5 


56 


01629 999S7 


08874 


99943 


o5ii7 


99869 


06860 99764 1 


0S600 


99680 


4 


ll 


01658 99986 


08408 


99942 


o5i46 


99867 


06889 


99762 


0S629 


99627 


1 


58 


01687 99986 


08482 


99941 


o5i75 


99866 


06918 


99760 


08658 


99625 


2 


59 
M 


01716 99985 


08461 
C.S. 


99940 


o52o5 


99864 


06947 
C.S. 


99758 

S. 


08687 
C.S. 


99622 
S. 


"u 


C. S. 1 s. 


S. 


C.S. 


s. 


89 Deo:. 


88 bejr. 


87 Dear. 1 


86 Deg. 1 


85 1 


>?. 



64 



A TABLE OF NATURAL SINES. 



i 

M 


5 Deg. 


1 6 Deg. 


7 l»eg. 


1 8 Deg. 


9 Deg. 




s. 1 c. s. 


1 ^• 


1 c. s. 


S. 1 C. S. 


1 s. 

13917 


C. S 


S. 1 c s. 


Im 


o 


087161 99619 


10453 


99452 


121871 99255 


99027 


1 15643 98769 


60 


I 


08745' 99617 


10482 


99449 


12216 99251 


13946 


99023 


15672; 98764 


59 


2 


08774 99614 


io5ii 


99446 


12245 99248 


13975 


99019 


15701 1 98760 


58 


3 


0SS03 


99612 


io54o 


99443 


12274! 99244 


14004 


990 ID 


i573oi 98755! D7I 


4 


o883i 


99609 


10569 
10597 


99440 


12302; 99240 


14033 


99011 


ID758 


98751! 56 1 


5 


08860 


99607 


99437 


12331 99237 


14061 


99006 


15787 


98746 


55 


6 


08889 
08918 


99604 


10626 


99434 


12360 99233 


14090 


99002 


1D816 


98741 


54 


I 


99602 


10655 


99431 


i238o| 99230 
12418 99226 


14119 


98998 


15845 


98737 


53 


08947 


99599 


10684 


99428 


14148 


98994 


15873 


98732 


52 


9 


08976' 99596 


10713 


99424 


12447 99222 


14177 


& 


15902 


987.28 


5! 


10 


O90o5| 99394 


10742 


99421 


12476 99219 
i25o4' 99213 


i42o5 


15931 


98723 


5o 


11 


090341 99591 


10771 


99418 


14234 


98982 


15959' 98718 


% 


12 


09063 


99588 


10800 


99415 


12533 


99211 


14263 


98978 


1598^' 


98714 


i3 


09092 


99586 


10829 
10858 


99412 


12562 


99208 


14292 


98973 


16017 


98709 


47 


14 


09121 


99583 


99409 


12591 


99204 


14320 


98969 


16046 


98704 


46 


ID 


09i5o 


99580 


10887 


99406 


12620 


99200 


14349 


98965- 


16074 


98700 


45 


i6 


09179 
09208 


99578 


10916 


99402 


12640 


99197 


14378 


98961 


i6io3 


98695 


44 


;? 


99575 


10945 


99399 


12678 


99193 


14407 


98957 


i6i32 


98690 


43 


09237 


99572; 


10973 


99396 


12706 


99189 


14436 


98953 
98948 


16160 


98686 


42 


19 


09266 


99570; 


11002 


99393 


12735 


99186 


14464 


16189 


98681 


41 


20 


09293! 99567' 


iio3i 


99390 
99386 


12764 


99182 


14493 


98944 


1621S 


98676 


40 


21 


093241 99364: 


11060 


12793 


99178 


14522 


98940, 


16246 


98671 


u 


22 


09353' 99362 


11080 
11118 


99383 


12822! 99175 


14551 


98936 


i62-'5 


98667 


23 


093S2 


99559 


99380 


i285i| 99171 


14580 


98931 


i63o4 


98662 


37 


24 


0941 1 


99556j 


11147 


99377 


12880 99167 


14608 


98927! 


16333 


98657 


36 


25 


09440 


99553 


11176 


99374 


1 2908 99163 


14637 


98923 


i636i 


98652 


35 


26 


09469 


9955i 


11205 


99370 


12937 99160 


14666 


98919: 


16390 


98648 


34 


27 


0949S; 99348^ 


11234 


99367 


129661 99 1 56 j 


14695 


98914; 


16419 


9S643 


33 


28 


09327 


99545 


11263 


99364' 


12995; 99152 


14723 


98910 


16447 


98638 


32 


29 


09556 


99542! 


11291 


99360, 


i3o24 


99148'; 


14752 


98906 


16476 


98633 


3i 


So 


09535 


99540 


ll320 


99357i 


i3o53 


99144' 


14781 


98902 


i65o5 


98629 


5o 


3i 


09614 


99537! 


11349 


99354] 


i3o8i 


99141' 


14810 


98897 


16533 


98624 


29 


32 


09642 


99534; 


11378 


99351 1 


i3iio 


9913- 


14S38 


98893 


16562 98619I 28 


33 


09671 


99531: 


11407 


99347 


i3i39 


99133^ 


14S67 


98889 


16591 98614 27 


34 


09700 


99528; 


11436 


99344; 


i3i68 


99129I 


14896 


^To^\ 


16620 


98609 


26 


35 


09720 
09758 


99526; 


11465 


99341 


I3i97 


99123; 


14925 


98880 


16648 


98604 


25 


36 


99523 


11494 


99337 


13226 


99122I 


14954 


98876 


16677 


98600 


24 


37 


09787 


99520 


ii523 


99334 


13254 


99118; 


14982 


98871 


16706 


98595 


23 


38 


09816 99517; 


11552 


99331 


13283 


99114! 


i5oii 


98867 


16734 


llUl 


22 


39 


09843 99514; 


ii58o 


99327 


13312 


99110I 


i5o4o 


98863 


16763 


21 


40 


09874 9951 1 1 


11609 
11638 


99324I 


13341 


99106: 


15069 


98858 


16792 


98580 20 


41 


09903 1 99508, 


99320 


13370 


99102! 


i5o97 


98854' 


16820 


98575 19 
98570 18 


42 


09932 99506 1 


11667 


99317 


13399 


99098; 


13126 


98849 


16849 
16878 


43 


09961 


99503; 


11696 


9^314 


13427 


99094' 


i5i55 


9??45| 


98565 17 


44 


09990 


99300: 


11725 


99310 


13456 


99091! 
99087; 


i5i84 


98841 


16906 


98561 16 


45 


10019 


99497 


11754 


99307 


13485 


l5212 


98836 


16935 


98556 i5 


46 


10048 


99494 


11783 


993o3 


i35i4 


99083; 


15241 


98832! 


16964 


985Dii 14 


47 


10077 


99491 


11812 


99300 


13543 


99079; 


15270 


"^fo't' 


16992 


985461 i3 


48 


10106 


99488 


11840 


99297 


13572 


99073 


15292 


98823 


17021 


9S541! 12 


49 


ioi35 


99485 


11869 
11898, 


99293! 


i36oo 


99071' 


15327 


98818 


i7o5o! 98536] 11 


5o 


10164' 99482! 


99290; 
99286! 


13629 99067 


15356 


98814' 


17078 98531; 10 


5i 


10192' 99479' 


11927: 


13653! 99063 


15335 


93809' 


171071 98526 


t 


52 


1022 1 99476 


11956 


99283! 


13687- 99059 


15414 


98803 


I7i36| 98521 


53 


10250 99473 


11985; 99279; 


13716 99053 


15442 


98800 


17164 9S5.6 


7 


54 


10279 99470 


12014 992761 


13744 


9905 I; 


15471 


98796 


17193I 98311 


6 


55 


io3o8 99467' 


12043 992721 


13773 


99047 


i55oo 


98701 
98787 


17222! 98506 


5 


56 


10337 99464 


12071; 99269! 


i38o2 


99043 


15529 


17250I 98301 


4 


u 


10366 99461 


1 2 100 99263] 


i333i 


qqo3q 


15557 


98782; 


17279' 98496 


3 


10395 99458! 


12129 99262! 


i586o 99035 


15586 


98778! 


1730S; 98491 
17336 Q8486 


2 


59 

M 


10424; 99^55; 

c. s. i S. 1 


121 58 99258 
C. S. 1 s. 


13889 9903 1 [ 


i56i5 


98773 

S. ! 


I 


C. S. 1 s. 


C. S. 


c. s. s. 


84 Deer. 1 


83 I 


)ecr. 1 


82 Deer. 


81 Deg ! 


80 1 


)e« 1 



A TABLE OF NATURAL SINES. 



65 



M 


10 Deg. 


11 Deg. 1 


12 Deg. 1 


13 De-. 1 . li Deg. j 




S. 


c. s. 


S. 


c. s. 


S. 


as. 1 

978i5; 


s. 1 c. s. 1 s. 


c. s. 


M 





17365 


98481 1 


19081 


98168: 


20791 


22495! 9743711 24192 


97080 


'6oi 




17393 


98476 


\l\?s 


98157^ 


20820 


97809 


22023 


97480 


24220 


97028: DO 

97015 58 


2 


17422 


98471 


98152 


20848 


97808, 


22552 


97424 


24249 


3 


17451 


98466 
98461 


19167 


98146 


20877 


97797! 


2258o 


974171 


24277 


97008 57 


4 


17479 


19193 


98140 


20905 97791 1 


22608 


97411 


24805 


97001 56 


5 


17508 984551 


19224 


98i85i 


209331 977»4 


22687 


97404 


24383 


96994 55 


6 


1-537 98450! 


19252 


98129! 


20962 97778 


22665 


97398 


24862! 96987I 54 


7 


17565 


98445 


19281 


98124! 20990! 97772 


22698 


97391: 
97384' 


24390 96980; 53 


8 


17594 


98440 


19309 


98118 


21019' 97766 


22722 


24418 969781 02 
24446 96966! 5i 


9 


17623 


98435 


19338 


98112 


21047 97760^ 


22750 


97878 


10 


17651 


98430 


19366 


981071 


21076 97754' 


22778 


97871!! 24474! 96959! 5ol 


n 


17680 


98425; 


19895 


98101 


2 II 04! 97748' 


22807 


97865 - 


240081 96902] 40 1 


12 


17708 


98420 


19423 


98096; 


21182 97742; 


22885 


97358 


24581 


96945; 48 1 


i3 


17737 


9^414 


19452 


980901 
98084 


21 161 97735; 


22868 


97351; 


24509 


96937 


47 


i4 


17766 


98409! 


19481 


21189 97729; 


22892 


97345 


245S7 


96980 


46 


i5 


17794 


98404 


19509 


98079 


21218 


97723 


22920 


97338 


24615 


96923 


45 


i6 


17823 


98399 


19538 


98073 


21246 


97717 


22948 


97331 


24644 


96916 


44 


\l 


17852 


98394! 
98389 
98383 


19066 


98067 


21275 


97711 


22977 


97325 


24672 


96909 


43 


17880 


19595 


98061 


2i3o3 


97705 


23oo5 


97318 


24700 




42 


19 


17909 


19623 


98o56 


2i38i 


97698 


28088 


97311 


24728 


96894 


41 


20 


17937 


98378 


19652 


98o5o| 


21860 


97602! 
97686! 


28062 


97304 


24756 


96887 


40 


21 


17966 


98373 


19680 


98044; 


21388 


28090 


97298 


24784 


96880 


89 


22 


17995 


98368 


19709' 98089 


21417 


97680! 


28118 


97201 
972b4 


24818 


96873 


38! 


23 


18023 


98362 


19737 98033] 


21445 


97673; 


28146 


24841 


9-6866 


37 1 


24 


i8o52 


98357 


19766 980271 


21474 


97667 


28175 


97278 


24869 


96808 


361 


25 


18081 


98352 


19794 9802 1 j 


2l502 


97661 


23203 


97271 


24897 


96851 


35 


26 


18109 


98347 


19823 


98016 


2i53o 


97655 


23281 


97264 


24925 


96844 


34 


27 


i8i38 


98341 


19851 


98010 


21559 


97648 


28260 


97257 


24953 


96887 


33 


28 


18166 


98336 


19880 


98004! 


2 1 587 


97642 


28288 


97251 


24982 


96829 


32 


29 


18195 


98331 


19908 


97998' 


2I6I6 


97636! 


283i6 


97244 


25oio 


96822 


31 


30 


18224 


98325 


19937 


97992 


21644 


97680 


28840 


97287 


25o38 


96815 


3o 


3i 


18252 


98320 


19965 


97987 


21672 


97628 


28873 


97280 


25o66J 96^07 


29 


32 


18281 


983i5 


19994 


97981 


21701 


97617 


28401 


97228 


250941 9680L 


28 


33 


i83o9 


983io 


20022 


97975 


21729 


9761 1 


28429 


97217 


25l22 


96793 


27 


34 


18338 


983o4 


2oo5i 


97969' 


21758 


97604 


28458 


97210 


25i5i 


96786 


26 


35 


18367 


98299 


20079' 97963 


21786 


97598 


23486 


97208 


20179 


96778 


25! 


36 


18395 


& 


20108, 97958 
20i36' 97952 


21814 


97592 


285i4 


97196 
97189 


25207 


96171 


24 1 


37 


18424 


21843 


97585 


23542 


25235| 96764 


23 


38 


18452 


98283 


20165 97946 


21871 


97579 
97073 


23571 


97182 


25263 96756 


22 


39 


1 848 1 


98277 


201931 97940 


2 1890 
21928 


28599 


97176 


25291 1 96-49 


21 


3o 


i85o9 
18538 


98272 


20222I 97934 


97566 


28627 


97169 


20820' 96742 


20 


41 


98267 


2025o' 97928 


21956 


97560 


28656 


97162 


25348: 96784 


\t 


42 


18567 


98261 


20279, 97922 


21985 


97558 

97347 


28684 


97155 


25376!. 96727 


43 


18595 


98256 


2o3o7 


97916 


220l3 


28712 


97148 


25404! 96719 


17 


44 


186241 98250 


20336 


97910 


22041 


97541 


28740 


97141 


25482! 96712 


16 


45 


18652 98245 


20364 


97905 


22070 


97534 


23769 


97184 


25460| 96705 


i5 


46 


18681 98240 


20893 


97899 


22098 


97528 


23797 


97127 


25488' 96697 


14 


47 


18710 98234 


20421 


97893 


22126 


97521 


28825 


97120 


255i6! 96690 
25545. 96682 


i3 


48 


18738 98229 


2o45o 


97887 


22155 


975i5 


28853 


97113 


12 


49 


18767! 98223 


20478 


97881 


22183 


97508 


28882 


97106 


255781 96675 


11 


5o 


18795; 98218 


2o5o7 


97875 


22212 


97502 


23910J 97100 


25601 96667 


10 


5i 


18824! 98212 


20535! 97869 
20563 97863 


22240 


97496 


289881 97098 
23966! 97086 


25629! 96660 


? 


52 


18852! 98207 


22268 


97489 


256571 96653 


53 


18881} 98201 


20592! 97857 


22297 


97483 


28995; 97079 


25685 96645 


7 


54 


18910' 98196 


20620 97851 


22825 


97476 


24028 97072 


25718; 96688 


61 


55 


18938: 98190 


20649 97845 


22353 


97470 


24o5i 97065 


25741 1 96680 


5 


55 


18967' 98 1 85 


20677I 97889 
20706! 97833 


22882 


97463 


24079 97o58 
24108^ 97o5i 


25769 96623 
25798 96615 


4 


57 


18995 981-9 


22410 


97457 


^i 


58 


19024 98174 1 20734' 97827 


22488 


97450 


24186 97044 


25826 q66o8 


2 


59 
M 


19052 98168 1 20763 97821 


2 2467 1 97444 


24164 97087 


25854 96600 


I 


C. S. 1 s. 


1 C. S. 1 s. 


C. S. 1 s. 


C. S. 1 s. 


C. S. i s. 


H 


79 Deg. 


1 78: 


Deor. 


77 Deg. 


76 Deg. 


1 75] 


Deg. 


-.- 



6b 



A TABLE OF NATURAL SINES. 






15 Deg. 


16 Leg. 


17 


Deg. 


1 IS 


Deg. 


19 


Deg. 


M 


S. 1 c. s. 


S. 


c. s. 


S. 


C. S. 


1 '^• 


C. S. 


S. 


1 S.C. 


25882 96593 


27364 


96126 


29287 


9563o!' 80902 


95106 


32557 


94552 


"67, 


I 


25910 96585 


27592 


96118 


29263 


93622 ! 30929 


95097 


32584 


94542 


It 


2 


25938 96578 


27620 


96110 


29298 


95618 80957 


95088 


I 32612 


94533 


3 


25966! 96570 


27648 


96102 


29821 


956o5 i 80985 


95079 


1 82689 


94528 


57 


4 j 20994 96362 


27676 


96094 


29848 


95396 ' 3lOI2 
95588' 31040 


95070 


j 82667 


94514 


56 


5 I 26022, 96555 


27704 


96086 


29876 


95061 


1 32694 


94304 


55 


6 •. 26c5o' 96547 


27731 


96078!! 29404 


95579! 3io68 


95o52 


32722 


94495 


54 


7 j 26079: 96540 


27759 


96070 


29482 


95571 i 81095 


95048 


32749 


94483 


53 


8 


261071 963^2 


27787 


96062 


29460 


95562' 31128 


95088 


32777 


94476 


52 


9 


26i35| 96524 


27815 


96054 


29487 


95554 1 3ii5i 


95024 


82804 


94466 


5i 


10 


26i63j 96517 


27843 


96046 


29315 


95545 


31178 


95oi5 


82882 


94437 


5o 


11 


261 91 ! 96009 


27871 


96087 


29348 


95586 


3.206 


95006 


32859 


94447 


49 


12 


26219; 96502 


27899 


96029 


2937, 


9552S 


8.238 


94997 


32887 


94438 


48 


i3 


26247 i 96494 


27927 


96021 


29599 


93519 


81261 


94988 


82914 


94428 


47 


14 


26275! 964H6 


27933 


96013 


29626 


95511 


81289 


94979 


82942 


94418 


46 


i5 


263o3 


96479 


27983 


96005 


29654 


93502 


3i8.6 


94970 


32969 


94409 


45 


16 


2633 1 


96471 


28011 


95997 


29682 


95408 


81844 


94961 


32997 


94899 


44 


17 


26339 


96463 


28089 


95989 


29710 


93485 


8.37-. 


94952 


33024 


94890 


43 


18 


26887 


96456 


28067 


95981 


29787 


954^6 


31899 


94948 


33o5i 


94880 


42 


^9 


264J5 


96448 


28095 


95972 


29765 


95467 


31427 


94988 


88079 


94370 


41 


20 


26443 


96440 


28128 


95964 


29793 


95439 


81454 


94924 


33 106 


94861 


40 


21 


26471 


96433 


28i5o 


95956 


29821 


95450 


81482 


949.5 


38184 


q485i 


39 


22 


26500 


96425 


28178 


95948 


29849 


95441 


3.5io 


94906 


33i6i 


94342 


38 


23 


26528I 96417 


28206 


93940 


29876 


95483 


8.537 


94897 


88189 


94882 


37 


24 


26556,' 96410 


28284 


95981 


29904 


95424 


3i565 


94888 


88216 


94822 


36 


25 


26584 


96402 


28262 


95923 


29982 


93415 


81598 


94878 


33244 


948.3 


35 


26 


26612 


96394 


28290 


95915 


29960 


95407 


81620 


94869 


3327. 


94308 


34 


27 


26640 


963S6 


2b8i8 


95907 


29987 


95898 


316/13 


94860 


88298 


94298 


33 


28 


26668 


96379 


28846 


9589b 


3ooi5 


95889 


81675 


9485, 


33826 


94284 


32 


29 


26696 


96371 


28874 


95890 


30043 


958801 


81708 


94842 


38858 


•94274 


3i 


3o 


26724 


96363; 


28402 


95882 


30071 


95372 


31780 


94882 


33381 


94264 


3o 


3i 


26752 


96355 


28429 


95874' 


30098 


95868 


3.758 


94828 


88408 


94234 


It 


32 


26780 


96347 


28457 


95S65 


30126 


95854 


8.786 


94814 


33436 


94245 


33 


26808 


96340 


28485 


95857 


30154 


93845 


8.8.8 


94805 


33468 


94285 


27 


34 


26836 


96332 


285i8 


95849 


30182 


93887 


81841 


94795 


33490 


94223 


26 


35 


26864 


96324 


28541 


95341 


30209 


95828 


3.868 


94786 


33518 


94215 


25 


36 


26892 


96816 


28569 


95882 


30287 


93819 


81896 


94777 


38545 


94206 


24 


37 


26920 


96808 


28597 


95824 


30265 


958.0 


3.928 


94768 


33573 


94.96 


23 


38 


26948 


96801 


28625 


95816 


30292 


95801 


8.951 


94758 


88600 


94186 


22 


39 


26976 


96293, 


28652 


95807 


80820 


93298 


81979 


94749 


88627 


94.76 


21 


40 


27004 


96285 


28680 


95799 


30348 


95284 


82006 


94740 


33655 


94.67 


20 


41 


27032 


96277 


28708 


95791 


30376 


95275 


82084 94730; 


38682 


94137 


\l 


42 


27060 


96269 


28786 


95782 


30408 


95266 


82061 94721 


33710 


94147 


43 


27088 


96261 


28764 


95774 


80481 


93257 


32089I 94712 


38787 


94.37 


'1 


44 


27116 


96253 


28792 


95766 


80459 


95248 


82116 94702 


88764 


94.27 


16 


45 


27144 


96246 


28820 


95737 


30486 


95240 


32144; 94693 


33792 


94118 


i5 


46 


27172 


96288 


28847 


95749 


3o5i4 


95281 


32171 94684' 


33819 


94108 


u. 


47 


27200 96230I 


28875 


95740 


30542 


95222 


82.99 94674: 


33846 


94098 


i3 


48 


27228, 96222 


28908 


93782 


30570 


952.8 


82227 94665 


88874 


94ob8: 12 


49 


27256 96214' 


2898. 


93724 


30597 


95204! 


82254 94656 


8890. 


94078' II 


5c 


272841 96206: 


2S959 


95715 


3o6?5 


93195, 


82282 94646 


88929 


94068 


10 


5i 


273l2j 9619S 


289S7 


95707 


3o653 


95186 


82809 94637 


88936 94038 


I 


52 


27340i 961901 


29015 95698 


306S0 


9517- 


32887 94627 


33988 94049 


53 


27368j 96182} 


29042 95690 


30708 


95.68 


82864 94618 


34011 94089 


1 


54 


27396! 96174' 


29070 95681 


30786 


95159 


82892 94609 


34038 


94029 


6 


55 


27424; 96166 


29098; 95678 


30763 


95i5o; 


82419 94599 


34065 


940.9 


5 


56 


27452; 96158 


29126! 93664 


30791 


951421 


82447 


94390 


34093 


94009 


4 


57 


27480I 961 5o1 29154! 936561 


30819 


95188 


32474 


94580 


34120 


98999 


3 


58 


27508, 96142, 
27536 96134 


291821 Q3647 


30846 


95124' 


82502 


94571 


34147 


989S9 


Z 


59 


29209 95689! 
C. S. 1 s. 


30874 


95ii5j 


82529 


94561 


34175 


989-9 
S. 
)eg. 


11 


M 


c. s. 1 s. 


C. S. 
72 1 


S. 
)eg. 


C. S. 


S. 


C. S. 
70 1 




74Deg. 1 


73 Deg. 


71 Deg. 



A TABLE OF NATURAL SINES. 



67 



M 


20 Deg. 


21 Deg. 


22 Deg. 


23 Deg. 


24 Deg. 


M 


S. 


C.S. 


S. 
35837 


C.S. 
93358 


S. |C. S. 


S. 


C.S. 


S. 1 c. s. 


o 


34202 


93969 


37461 92718 


39073 


92o5o 


40674 


91355 


60 


I 


34229 


93959 


35864 


93348 


37488 92707 


39100 


92039 


40700 


91343 


5? 


2 


34237 


93949 


35891 


93337 


37515 92697 


39127 


Q2028 


40727 
40753 


9i33i 


3 


34284 


93939 


35918 


93327 


37542 92686 


39153 


92016 


91 3 19 


57 


4 


343 1 1 


93929 


35945 


93316 


37569 9:675 


39180 


92005 


40780 


91307 


56 


5 


3<339 


Q3919 


35973 


93306 


37595 92 64 


39207 


91994 


40806 


91295 


55 


6 


3i366 


93909 


36000 


93295 


37022 92053 


39234 


91982 


40833 


91283 


54 


I 


34393 


36027 


93285 


37649, 92642 


39260 


91971 


40860 


91272 


53 


34421 


93889 


36o54 


93274 


37676 


92631 


39287 


91959 


40886 


91260] 52 


9 


34448 


93879 


36o8i 


93264 


37703 


92620 


39314 


91948 


40913 


Q1248 


5i 


ic 


34475 


93869 


36io8 


93253 


37730 


92609 


39341 


91936 


40939, 91236 


5o 


,u 


345o3 


93859 


36i35 


93243 


^77^7 


90598 


39367 


91925 


40966 


91224 


g 


12 


34530 


93849 


36162 


93232 


37784 


92587 


39394 


91914 


40992 


91212 


i3 


34557 


?3839 


36190 


93222 


37811 


92076 


39421 


91902 


41019 


91200 


47 


i4 


34584 


93829 


36217 


93211 


37838 


92060 


39448 


91891 


41045 


91188 


46 


i5 


34612 


93819 


36244 


93201 


37865 


92554 


39474 


91879 


41072 


91176 


45 


i6 


34639 


93809 


36271 


93190 


37892 


92543 


39501 


91868 


41098 


91 164 


44 


\l 


34666 


93799 


36298 


93180 


37919 


92532 


39528 


9 1 856 


41125 


9ii52 


43 


34694 


93789 


36325 


93169 


37946 


92521 


39555 


91845 


4ii5i 


91140 


42 


19 


34721 


93779 


36352 


931 59 


37973 


92510 


39581 


91833 


41178 


91128 


41 


20 


34748 


93769 


36379 


93148 


37999 


92499 
92488 


39608 


91822 


41204 


91116 


40 


21 


34775 


93750 
93748 


36406 


93i37 


38026 


39635 


91810 


4i23i 


91104 


l^ 


22 


34803 


36434 


93127 


38o53 


92477 


39661 


91799 


41257 


91002 
91080 


23 


34830 


93738 


36461 


93116 


38o8o 


92466 


39688 


91787 


41284 


37 


24 


34857 


93728 


36488 


93106 


38107 


92455 


39715 


91775 


4i3io 


91068 


36 


25 


34884 


93718 


365i5 


93095 


38i34 


92444 


39741 


91764 


41337 


9io56 


35 


26 


34912 


93708 


36542 


93084 


38i6i 


92432 


39768 


91752 


41363 


91044 


34 


27 


34939 


93698 
93688 


36569 


93074 


38188 


92421 


39795 


91741 


41390 


91032 


33 


28 


34966 


36596 


93o63 


382i5 


92410 


3q822 


91720 
91718 


41416 


91020 


32 


29 


34993 


93677 


36623 


93o52 


38241 


92399 


39848 


41443 


91008 


3i 


30 


35021 


93667 


36650 


93042 


38268 


92388 


39875 


91706 


41469 


90996 


3o 


3i 


35048 


93657 


36677 


93o3i 


38295 


92377 


39902 


91694 


41496 


90984 


It 


32 


35075 


93647 


36704 


93020 


38322 


92366 


39928 


91683 


4l522 


90972 


33 


35102 


93637 


36731 


93010 


38349 


92355 


39955 


91671 


41549 


90960 


27 


34 


35i3o 


93626 


36758 


92999 
92988 


38376 


92343 


39982 


91660 


41570 


90948 


26 


35 


35i57 


93616 


36785 


3 8403 


92332 


40008 


91648 


41602 


90936 


25 


36 


35i83 


93606 


368i2 


92978 


38430 


92321 


4oo35 


91636 


41628 


90924 


24 


37 


352II 


93596 


36839 


92967 


38456 


92310 


40062 


91625 


4i655 


90911 


23 


38 


35239 


93585 


36867 


92956 


38483 


•92299 


40088 


91613 


41681 


?ol? 


22 


39 


35266 


93575 


36894 


92945 


385io 


92287 


4oii5 


91601 


41707 


21 


40 


35293 


93565 


36921 


92935 


??S'' 


92276 


40141 


91590 


41734 


90875 


20 


41 


35320 


93555 


36948 


92924 


38564 


92265 


40168 


91578 


41760 


90863 


\l 


42 


35347 


93544 


36975 


92913 


38591 


92254 


40195 


91566 


41787 


9085 1 


43 


35375 


93534 


37002 


92902 


38617 


92243 


40221 


91555 


41 81 3 


90839 


17 


44 


35402 


93524 


37029 


92892 
92881 


38644 


92231 


40248 


91543 


41840 


90826 


16 


45 


35429 


93514 


37056 


38671 


92220 


40275 


9i53i 


41866 


90814 


i5 


46 


35456 


935o3 


37083 


92870 


38698 


92209 


4o3oi 


91519 


41892 


90802 


14 


47 


35484 


93493 
93483 


37110 


92859 


38725 


92108 


40328 


9i5o8 


41919 
41945 


90790 


i3 


48 


355II 


37137 


92849 


38752 


92186 


40355 


91496 


90778 


12 


49 


35538 


93472 


37164 


92838 


38778 


92175 


4o38i 


91484 


41972 


90766 


II 


5o 


35565 


93462 


37191 


92827 


388o5 


92164 


40408 


91472 


41998 


90753 


10 


5i 


35592 


93452 


37218 


92816 


38832 


92l52 


40434 


91461 


42024 


907 4 i 


? 


52 


35619 93441 


37245 


92805 


38859 


92I4I 


40461 


91449 


42o5i 


90729 


53 


35647 


93431 


37272 


92794 
92784 


38886 


92i3o 


40488 


91437 


42077 


90717 


7 


54 


30674 


93420 


37299 


38912 


92119 


4o5i4 


91425 


42104 


90704 


6 


55 


35701 


93410 


37326 


92773 


38939 


92107 


4o54i 


91414 


42i3o 


90692 


5 


56 


35728 


93400 


37353 


92762 


38966 


92096 


40567 


91402 


42156 


90680 


4 


57 35755 


93389 


37380 


92751 


38993 


92ort5 


40594 


91390 


42183 


9°5^? 


3 


58 


35782 


93379 
93368 


37407 


92740 


39020 


92073 


40621 


91378 


42209 
42235 
C.S. 


90655 


2 


9q 


35810 


37434 
C.S. 


92729 


39046 


92062 


40647 


91366 


90643 


I 


C.S. 


S. 


S. 


C.S. 


S. 


C.S. 


S. 


S. 


"M 


69 De^. 


68 Peg. 


67 Deg 1 


66 Deg. \ 


65 Deg. 1 



19 



6S 



A TABLE OF NATURAL SIXES. 



M 


25 Dc-g. 


26 Deg. 1 27 Deg. i 28 Deg. 


29 Dog. 


1 


S. ' C. S. 


S. 


C. S. || S. i c. s. 1} s. 


c. s. 1 


S. 


C. S. 


M 


o 


42262 9063 1 


43837 


89S79 1 45399 89IOI j 46947 


882951 


4B481 


87462 


60 


I 


42288i 90618 


43863 


898671 40420 89087! 46973 


88281 


485o6 


87448 5o 
87434 53 


3 


423 1 5j 90606 


43SS9 


89804: 40451 89074 46999 


88267' 


48532 


3 


42341 


90094 


43916 


89S4I 1 45477 89061 47024' 88204 


48557 


87420 57 


4 


43367 


9o5S2 


43942 


89828! 40003 89048 47o5o; 88240 


48583 


87406 56 


5 


42394 


90569 


43968 


898161 40529' 89035 i 47076 


88226; 


48608! 87391 


55 


6 


42420 


90507 


43994 


89S03 ' 40554 89021! 47101 


88213; 


48634 


87377 


54 


I 


42446 


90545 


44020 


S9-90 ! 40080 89008^ 47127 
89777 40606 889951 47153 


88199' 


48659 


87353 53 


424731 90532 


44046 


88i85 


48684 


87349 52 


9 


42499 90320 
4252DJ 90007 


44072 


89764: 40632 88981 1 47178 


88172: 


48710 


87335 


5i 


10 


4409S 


89752 1 45658: 88968 47204 


88153; 


48735 


87321 


5o 


II 


42552' 90495 


44124 


89739 45684 88955 47229 


88144: 


48761 


87306 


it 


12 


425781 904S3 
42604I 904-0' 


44i5i 


89726 457101 88942 47250 


88i3oi 


48786 


87292 


i3 


44177 


89713 45736 88928 ! 47281 


88117: 


4881 1 


87278 


47 


14 


42631 


90458' 


44203 


89700 1 45762 88915 


47306 


88io3, 


48837 


87264 


46 


i5 


42607 


90446 


44229 


89687 J 45787 88902: 


47332 


88089 1 


48862 


87250 


45 


i6 


42683 


90433 


44255 


89674' 


458i3 88888 


47358 


88075 


48888 


87235 


44 


\l 


42709 


90421 1 


44281 


89662 


45839 88875 
45860! 88862 


47383 


88062! 


48913 


87221 


43 


42736 


90408! 


44307 


89640 


47409 


88048, 


48938 


87207 


42 


*9 


42762 


90396! 
903831 


44333 89636 


45891! 88848 


47434 


88034 ' 


48964 


87193 


41 


20 


42788 


44359 


89623; 


45917 


88835 


474601 88020 


48989 


87178 


40 


21 


42815 


90371 


443S5 


89610 1 43942 


88822 


47486 1 88006^ 


49014 


87164 


39 
38 


22 


42841 


90358! 


4441 1 


89097 


45968 


88808 47511! 87993 


49040 


87100 


23 


42S67 


90346: 


44437 


89584: 


4O994 


88795 47537I 87979 


490&5 


87136 


Q-, 


24 


42894 


90334' 


44464 


89571: 


46020 


88782 47562: 87960 


49090 


87121 


36 


25 


42920 


9o32i: 


44490 


89558 


46046 


88768 1 4708S' 87951: 


49116 


87107 


35 


26 


42946 


90309' 


44016 


89545 


46072 


88755 


4-614; 87937 


49141 


87093 


34 


27 
28 


42972 


90295^ 


44542 


89532 


46097 


88741' 


47639 87923; 


49166 


87079 


33 


42999 


90284 1 


44568 


89519; 


46123 


88728' 


47660; 87909; 


49192 


87064 


32 


29 


4302D 


90271 i 


44594 


895o6i 


46149 


887i5j 47690! 87896] 


49217 


87o5o 


3i 


3o 


43o5i 


90259J 


44620 


89493, 


46170 


88701; 


47716 87882 


49242 


87036 


30 


3i 


43077 


90246; 


44646 


89480' 


46201 


88688! 


47741 1 87868: 


49268 


87021 


29 


32 


43104 


90233 


44672 


89467; 


46226 


88674: 


47767; 87854 


49293 


87007 


23 


33 


43i3o 90221: 


44698 


89404 


46252 88661' 
46278 88647i 


47793; 87840 
47818 87826; 


49318 


86993 


27 


34 


43 1 56 


90208: 


44724 


89441' 


49344 


86978 


26 


35 


43182 


90196' 


44700 


8942S: 


46304 88634' 


47844 87812! 


49369 


86964 


25 


36 


43200 


90183 


44776 


89415; 46330 


88620: 


47869; 8779S! 


49394 


86949 


24 


37 
38 


43235 


901711 


44802 


89402: 46355 


88607' 


47890^ 87784; 


49419 


86930 


23 


43261 


901 58 1 44828 


893S9' 


46381. 88593 


47920 87770; 


49440 


S6921 


22 


39 


43287 


90146 'i 44854 


89376^ 


46407 88580 


4-946 87756. 


49470 


86906 


21 


40 


433i3l 90i33:i 44S80 


89363 


46433 88566 
46408 88553 


47971^ 877431 


49490 


86892 


20 


41 


43340 


90120 44906 


89350' 


47997 87729' 


49521 


86878 


;i 


42 


43366 


90108 1 44932 


89337: 


46484I 88539; 


48022 877151 


49546 


86863 


43 


43392 


900^5; 
90082: 


44958 


89324; 


465io 


88526 


48048 87701! 


49571 


86849 


17 


44 


43418 


44984 


89311I 


46536 


885i2 


48073 87637; 


49596 


86334 


16 


45 


43445 


90070 


45oio 


89293 


46561 


88499, 


48099^ 876731 


49622 


86320 


i5 


46 


43471 


90057 1 


45o36 


89285; 


46587 


88485; 


48124' 87659! 


49647 


868o5 


14 


S 


43497 


90045 1 


40062 


89272 


46613 


88472 


43i5o 87645; 


49672 


86791 


i3 


43523 


90032: 


45o88 


89209' 


46639 


88458; 


48175 87631 11 49697 


K"'!" 


12 


49 


43549I 9C019; 


40114 


89245, 


46664 


88445] 


48201 87617, 


49723 


86762 


11 


00 


43573, 90007; 


40140 


89232! 


46690 


8843 1 i 


48226, 87603! 


49748 


86748 





5i 


43602 


899^4 45i66 


89219I 


46716 


8841 7 j 


48252 87589! 


49773 


86733 


g 


52 


43628 


S99bij 45192 


89206I 


46742 


88404; 


48277! 875701 


49798 


86719 


fe 


53 


43554 


89968 , 40218 


46767 
46793 


88390 


483o3 87561 


49824 


86704 


I 


04 


43680! 89906 1 40243 


88377 


43323 


87546; 


49849 
49874 


86690 


55 


43706 


89943, 40269 


89167 


46819 


88363, 


48354 


87532; 


86670 


5 


56 


43733 


89930 45290 


89i53i 


45844 


88349 


48379 


87518 


49899 


86661 


i 


U 


g?i? 


89918J 45321 


89U0; 


46870 


88336 


48400 


87504! 


49924 


86646 


3 


89905; 45347 


89127, 


46896' 88322! 


48430 


87490' 


49939 


86632 


2 


59 


43811 


89892 


45373 


891 14 


46921! 883o8i 


48406 


87476: 


49970 


86617 


I 
M 


M 


c. s. 


S. 


C. S. 


S. 1 


c. s. 1 s. 1 


C. S. 


S. i| c. s. 


S. 


C4Dosr. 


63 ] 


3c?. i 


62] 


3eg. I 


61 Deg. [| 60 ] 


^•_. 



A TABLE OF NATUKAL SINES. 



69 



M 


3U l>eg. 




b2 l>eg. 


33 


Deg. 


3^ Deg. 


M 


S. 


C.S. 


S. 


C.S. 
85717 


S. C. S. 


S. 


I C.S 


S. 


C.S. 


o 


50000 i 866o3 


5i5o4 


52992 84805 


54464 


8386^ 


559x9! 82904 


"60 


' 


5oo25 


86588 


5x529 


83702 


53ox7' 84789 


54488 


8385x 


55943; 82887 


It 


2 


5oo5o 


86573 


5 1 554 


83687 


53o4i 84774 


545 1 3 


83835 


55968, 8287X 


3 


50076 


86559 


5x579 


85672 


53o66 84759 


54537 


' 83819 ■-5992' 82855 


ll 


4 


5oioi 


86544 


5 1 604 


85637 


53091! 84743 


5456 X 


' 83804 


56oi6. 82839 


5 


50126 


86530 


51628 


85642 


53xx5, 84728 


54586 


' 83788 


56040' 82822 


55 


6 


5oi5i 


865 1 5 


5x653 


85627 


53x40 


84712 


546x0 


83772 


56o64' 82806! 54 


I 


50176 


86501 


5x678 


856x2 


53x64 


84697 


54635 


83756 


56o88 82790! 53 


5020I 


86486 


5i7o3 


85397 


53189 


84681 


546^9 


83740 


56ii2 82773: 53 


9 


50227 


86471 


5x728 


85582 


532X4 


84666 


54683 


83724 


56x36 82757! 5x 


lO 


50252 


86407 


5x753 


85567 


53238 


84650 


54708 


83708 


56i6o 8274X 5o 


II 


50277 


86442 


5x778 


8535X 


53263 


84635 


54732 


83692 


56x84 827241 49 
562o3 82708! 40 


12 


5o3o2 


86427' 


5x8o3 


85536 


53288 


84619 


54756 


83676 


i3 


5o327 


86413 


5x828 


85521, 


53312 


84604 


5478X 


83660 


56232 826921 47 


14 


5o352 


86398 
86384 


5x852 


83306 


53337 


84583 


54805 


83645 


56256 82675 


46 


i5 


5o377 


51877 


83491 


53361 


84573^ 


54829 


83629 


56280 82659 


45 


i6 


5o4o3 


86369' 


5x902' 


85476 


53386 


84557! 


54854 


836x3 


563o5 82643! 44 


\l 


50428 


86354 


5X927 


8546 X 


5341 1 ' 84542 


54878 
54902 


83397 
83581 


56329 82626! 43 


50453 


86340 


5x952 


85446 


53435 


84526 


56353 82610! 42 


19 


50478 


86325, 


5x977 


8543 1 


53460 


845xi; 


54927 


83565 


56377 825931 41 


20 


5o5o3 


863x0 


52002 


83416 


53484 


84495: 


5495X 


83549 


5640X 82577 40 


21 


5o528 


86295 


52026 


85401 


53509 


84480 


54970 


83533 


56425 8256x1 39 


22 


5o553 


86281; 


52o5x' 


85385 


53534 


84464 


54999 


835x7 


56449 82544' 38 


23 


50578 


86266, 


52076 


85370 


53558 


84448 


55o24 


835oi 


56473 825281 37 


24 


5o6o3 


8625i 


52x01' 


83353i 


53583 


84433 


55048 


83485 


56497 825xi| 36 


25 


50628 


86237 


52126; 


853401 


53607 


84417 


55072 


83469 


56521 82495: 35 


26 


5o654 


86222 


52x5x 


85325. 


53632 


84402 


55097 


83453 


56545 824781 34 


27 


50679 


86207 


52x75! 


853X0; 


53656 


84386 


55i2x 


83437 


56569 82462 33 


28 


50704 


86192 


52200 


85294; 


5368 X 


84370 


55x45 


83421 


56593 82446; 32 


29 


50729 


86178: 


52225 


83279' 


53705 


84355 


55169 


834o5 


566x7 82429! 3x1 


3o 


50754 


86x63, 


52250 


85264j 


53730 


84339; 


55x94 


833:39 


56641, 824x3 


3o 


3i 


50779 


86x48 


52275 


8p249 


53754 


84324 


552x8 


83373 


56665 82396 


ll 


32 


50804 


86x33; 


52299' 


85234 


53779 


84308; 


55242 


83356 


56689 82380 


33 


50829 


861x9 


52324' 


852x8 


53804 


84292' 


55266 


83340 


567x3 82363 


27 


34 


5o854 


86104 


5234Q 


85203 


53828 


84277! 


55291 


83324' 


56736 82347 


26 


35 


50879 


86089 


52374 


85 1 88 


53853 


8426X 


553i5 


833o8| 


56760 82330 


25 


36 


50904 


86074 


52399 


85x73 


53877 


84245: 


55339 


83292 


56784 823x4 


24 


37 


50929 


86009 


52423 


85x57 


03902 


84230 


55363 


83276 


568o8 82297 
56832 8228X 


23 


38 


50954 


86045 


52448 


85x42 


53926 


842x4 


55388 


83260 


22 


39 


50979 


86o3o' 


52473 


85x27 


5395X 


84198; 
84182! 


55412 


83244 


56856 82264 


2X 


40 


5 1 004 


86oi5 


52498 


85ix2 


53975 


55436 


83228; 


5688o 82248 


20 


41 


51029 


86000 


52322 


85096 
85o8i 


54000 


841671 


55460 


83212! 


56904 8223x 


XQ 

x8 


42 


5io54 


85985 


52547: 


54024 


84i5i: 


55484 


83x95 


56928 822x4 


43 


5io79 


85970' 


52572 


85o66 


54049 


84x35 


55309 


83x79 


56952 82198 
56976! 82i8x 


17' 


44 


51104 


85956; 


52597j 


85o5i 


54073 


84120: 


55533 


83x63 


161 


45 


5X129 


8594X 


5262 xj 


85o35 


54097 


84104; 


55557 


83x47 


57000: 82x65 


15; 


46 


5ii54 


85926 


52646' 


85o2o 


54x22 


84088' 


55581 


83i3i 


57034 82148 


14 


47 


5ii79 


859XX 

85896' 


526-7x1 83oo5i 


54x46 


84072 


556o5 


83xi5 


57047! 82X32 


x3 


48 


5i2o4 


52696; 


84989 


54x71 


84057 


5563o 


83098 


57071! ?2XX5 I2| 


49 


51229 


85881 ; 


52720 


84974 


54195 


84041' 


55654 


83o82 


57095 82098 IX ! 
57119' 82082 xo 


5o 


51234 


85866: 


52745 


84959 


54220 


84023; 


55678 
55702 


83o66 


5i 


51279 


85851 ' 


52770 


84943 


54244 


84009' 


83o5o 


57x43 82o65j 9 


52 


5i3o4 


85836 


52794 


84928! 


54269 


83994 


55726 


83o34 


57x67 82048 


81 


53 


5i329 


8582 x! 


52819 


849x3, 

84897 
84882! 


54293 


83978 


55750 


83017 


57I9X: 82032 


1 


54 


5i354 


858o6, 


52844 


543x7 


83962 


55775 


83oox 


572x5i 82oi5 


6 


55 


5i379 


85792 


52869 


54342 


83946! 


55799 


82985 


57238: 81999 


5 


56 


5x404 


85777 


52893 


84866! 


54366 


83930! 


55823 


82969 


57262' 81982 


4 


^2 


51429 


80762; 


52918 


84851 


5439 X 


83899! 
83883' 

S._ 1 


55847 


82953 


57286! 81965 


3 


58 


5x454 


80747; 


52943 


84836! 


544x5 


53871 


82936 


573x0 81949 


2 


59 


5x479 


85732; 


52967 


84820 


54440 


55895 


8292,0 


57334 81932 


"m 


M 


C.S. 


s. 1 


C. S. i 


S. 


C.S. 


C.S. 


S. 


C. S. 1 S. 




59] 


3e^. I 


58 De?. 1 


57 Dee. 1 


56 Deer. 1 


55 Eeg. 



70 



A TABLE OP NATURAL SINES. 



M 


35 Deg. 


36 Deg. 


37 


Dcg. 


38 Deg. 


39 Deg. 


M 


S. 


C. S. 
81915 


S. 


C. S. 


S. 
60182 


jC. S. 
j 79864 


S. 


C. S. 


S. 


0. S. 





57358 


58779 


80902 


^566 


7880. 


62932 


77715 


"60 


I 


57381 81899 


588o2 


80885 


60203 


79S46 


6.589 


78783 


62955 


77696 


59 


2 


57405 81882 


58826 


80867 


' 60228 


, 79829 


1 61612 


78165 


62977 


1 -77678 


58 i 


3 


57429 8i865 


58849 


8o85o 


' 60231 


1 79811 


6.635 


78747 


63000 


77660 


1 57 


4 


57453 81848 


58873 


80833 


60274 


! 79793 


6.658 


78729 


63022 


77641 


56 


5 


57477 8 1 83 2 


58896 


80816 


60298 


i 79776 


6.68. 


787.1 


63045 


77623 


! 55 


6 


1 57501 8i8i5 


58920 


80799 


60321 


79758 


61704 


78694 


63o68 


i 77603 


1 54 


7 i 57524 8179^ 


58943 


80782 


6o344 


79741 


6.726 


78676 


63090 


! 775% 


! 53 


8 ; 57548 


81782 


58067 


80763 


60367 


79723 


6.749 


78658 


631.3 


1 77568 


52 


9 57572 


81765 


58990 


80748 


60390 


79706 


6.772 


78640 


63.35 


77550 


5i 


ic 57596 81748 


59014 


80730 


60414 


79688 


61795 


78622 


63 1 58 


77531 


5o 


11 1 57619 81731 


59037 


80713 


60437 


79671 


618.8 


78604 


63. 80 


775i3 


49 


12 


57643 


81714 


59061 


80696 


60460 


79653 


61841 


78586 


63203 


77494 


48 


i3 


57667 


81698 


59084 


80679 


60483 


! 79635 


61864 


78568 


63225 


77476 


47 


14 


57691 


81681 


59108 


8.6j2 


6o5o6 


I 796J8 


6.887 


78550 


63248 


77438 


46 


ID 


57715 


81664 


59131 


80644 


60529 


79600 


61909 


78532 


63271 


77439 


45 


16 


57738 


81647 


59154 


80627 


6o553 


79583 


6.932 


785.4 


63293 


77421 


44 


17 


57762 8i63i 


59178 


80610 


60576 


79365 


6.955 


78496 


633.6 


77402 


43 


18 


57786 81 614 


59201 


80393 


60399 


79547 


61978 


78478 


63338 


77384 


42 


19 


57810 81397 


59223 


80376 


60622 


79530 


62001 


78460 


6336. 


77366 


41 


20 


57833 8i58o 


59248 


80338 


60643 


79312 


62024 


78443 


63383 


77347 


40 


21 


57857 


8i563 


59272 


8o54i 


60668 


79494 


62046 


78434 


63406 


77339 


39 
38 


22 


57881 


81546 


59293 


80334 


60691 


79477 


62069 78403 


63438 


77310 


23 


57904 


8i53o' 


59318 


80307 


60714 


79459 


62092I 78387 


63451 


77292 


37 


24 


57938 


8l5l3: 


59342 


80489 


60738 


79441 


62. .5 


78369 


63473 


77273 


36 


25 


57952 


81496; 


59365 


80472 


60761 


79434 


62.38 


7835. 


63496 


77255 


35 


26 


57976 


81479' 


593S9 


80455 


60784 


79406 


62160 


78333 


635.8 


77236 


34 


27 


57999 


81462, 


59412 


80438 


60807 


79388 


62.83 783.5 


63540 


77218 


33 


28 


58023 


8i445i 


59436 


80430 


6o83o 


79371 


622061 78297 


63563 


77.99 


32 


29 


58047 


81428: 


59439 


80403 


60853 


79353 


62229 78379 


63585 


77.8. 


3i 


3o 


58070 


81412: 


59482 


8o386 


60876 


79335 


6225i 78261 


636o8 


77.62 


3o 


3 1 


58094 


81395^ 


59306 


8o368 


60899 


793^8 


622-^' 78243 


63o3o 


77'44 


29 

28 


32 


58ij8 


81378: 


59329 


8o35i 


60922 


79300 


622971 7S225 


63653 


77.25 


33 


58i4i 


8i36i: 


59552 


80334' 


60945 


79282I 


62320 78206 


63675 


77.07 


27 


34 


58i65 


8i344' 


59376 


8o3i6^ 


60968 


792641 
79247I 


63342 78.88 


63698 


77088 


26 


35 


58189 


813275 


59399 


80299 


60991 


62365 78.70 


63730 


. 77070 


25 


36 


58212 


8i3io' 


59622. 


8028 a; 


6101 5 


79239: 


62388 78.52 


63743 


77031 


24 


37 


582.36 


81293; 


59646 


80264 


6io38 


79311! 


62411! 78.34 


63765 


77033 


23 


38 


58260 


81276! 


59669 
59693, 


80247 


61061 


79J93| 


62433 781 16 


63787 


77014 


22 


39 


58283 


81239! 


8o23o 


61084 


79.76 


62456 78098 


638.0 


76996 


21 


40 


583o7i 


81242! 


59716! 


80212! 


61 107 


79i5S 


62479 78079 


63832 


76977 


20 


41 


58330 


8l225| 


59739' 


80195! 


6ii3o 


79 "40 


62502 78061 


63854 


76939 


;? 


42 


58354 


8i2o8[ 


59763: 


80178! 


6ii53 


791231 


62324 78043 


63877 


76940 


43 


58378' 


81191 


59786' 


80160 


61176 


79105 


62347 78025 


63^99 7^03. 


17 


44 


58401 1 


81 174! 


59S09 


80143 


61199 


79087] 


62570 78007 


63922 


7<>.,)3| 


16 


45 


58425, 


8ii57| 


59832 


80125 


61222 


79069 


62392; 77988 


63944 


70)34 


i5 


46 


54449' 


811401 


59836 


80108 


61245 


7905 1 


626.5 77970 


63966 


76866 


14 


47 


584721 


31123^ 


59879 


80091 


61268 


790331 


62638 77932 


63989 


76847 


i3 


48 


58496; 


81106! 


59902, 


80073 


61291 


790i5i 


62660 77934 


640.1 


76828 


12 


49 


58519! 


81089? 


59926 


8oo56 


6i3i4 


789931 


62683 77916 


64033 


768.0 


II 


5o 


58543' 


81072; 59949I 


8oo38 


6.337 
6i36o 


78980I 


62706 77897 


64o56 


76791 


10 


5. 


58067! 


8l033| 


59972! 


80021 


78962! 


62728; 77879 


64078 


76772 


I 


52 


58390! 


8io38 


59995 


8ooo3 


6i383 


78944I 


6275.1 77861 


64100 


76754 


53 


586 1 4| 


81021 


60019 


799S6 


61406 


78926 


62774 77843 


641 231 


76735 


7 


54 


53637! 


81004 


60042 


79968 


61439 


78908 


62796: 77824 


64145 


767.7 


6 


55 


58661 i 


80987 


6oo65l 


79931 


6i45i 


78891 


628.9! 77806! 


64167 


76698 


5 


56 


58684' 


80970 


60089 79934' 


61474 


78873 


62842 


77788 


64190 


76679 


4 


57 


58708 


80953 


60112 799i6{ 


61497 


78855 


63864 


77769 


64212 


76061. 


3 


58 


587311 


80936! 


6oi35| 79899I 


6i52o 


78837 


63887 


7775.1 


64234 


76642 


2 


59 


58755 


80919J 

S. 


60 1 58 


7988. 
S. 


61 543 


78819 


62909 
C. S. 


77733 


64256 


76623 

S. 


I 
M 


M 


c. s. 1 


O.S.I 


C. S. 


S. 


S. 


C. S. 1 


54 Deof. 1 


53 Deg. 1 


52 I 


)esr. 


51 Deg. 1 


50 Deg. 1 



A TABLE OF NATUKAL SINES. 



Tl 



_M^ 


40 Deg. 

s. c. s. 


! 41 Deg. 


1 ^^ 


Deg. 


1 ^3 


Deg. 


1 44 Deg. 


M 
60 


S. 1 c. s. 

656o6 75471 


s. 1 c. s. 


S. IC. s. 


S. |C,S. 





642^9 76604 


66913; 743 14 


68200 73i35 


69466, 71934 


1 


6430II 76086 


i 65628 75452 


] 66935; 742951 68221; 73116^1 69487' 7I9I4 


! 5g 


3 


64323; 76367 


6563C 73433 i 66956I 74276 


68242 73096 j 69308! 71894 


5? 


3 


64346 76548 


, 63672 75414:1 66978; 74236 


68264 73076 6g529 


71873 


;s 


4 


64368: 7653o 


! 65694 75395 


66999: 74237 


68285 


, 73036 


69549 


7«853 


5 


64390' 765 1 1 


63716 75375 


6-02 li 74217 


683o6 


73o36 


1 69370 


' 71833 


55 


6 


64412 76492 


! 65-38 75356 


670431 74108 


68327 


730.6 


' 6959, 


! 7i3i3 


' 54 


7 


64435 76473 


: 63759 75337 


67064' 74178 


68349 


' 72996 


; 696.2 


! 71792 


' 53 


8 


644571 76455 


1 65781: 75318;! 67086 


74139 


68370 


i 72976 


i 69633 


; 71772 


52 


9 


64479 76436 


658o3 75299 


67107 


74139 


68391 


I 72937 


69654 


i 71752 


5i 


10 


645oi| 76417 


1 65825, 73280 


67129 


74120 


6S412 


72937 


69675 


71732 


5o 


II 


64524' 76398 


' 65847 75261 


67151 


74100 


68433 


; 72917 


69696 


71711 


% 


12 


64346 76380 


1 65869 75241 


67172 


74080 


68455 


i 72897 


69717 


71691 


i3 


64568 76361 


i 63891 75222 


67194 


74061 


68476 


; 72877 


69737 


71671 


ii 


U 


64590 76342 


' 63913 75203 


67215 


74041 


68497 


: 72857 


69758 


7i65o 


i5 


64612 76323 


1 65935, 75184 


67237 


74022 


685 18 


i 72837- 


69779 


7i63o 


45 


i6 


64635 76304 


1 65956 75i65 


67258! 74002 


68539 


' 72817 


69800 


71610 


44 


17 


64657 76286 


: 639-8 75146 


67280 


739^3 


68361 


72-97 


69821 


71590 


43 


i8 


64679 76267 


66000 75126 


67301 


73963 


68382 


1 72777 


69842' 71369 


42 


19 


64701 76248 


66022: 75107 


67323 


73944 


686o3 


1 72757 


69862 


71549 


41 


20 


64723 76229 


66044 75088 


67344 


73924 


68624 


1 72737 


69883 


7.529 


40 


21 


64746 76210 


66066 75069 


67366 


73904 


68645 


72717 


69904 


7i5o8 


ii 


22 


64-68 76192 


66088 75o5o 


67387 


73885 


6S666 


1 72697 


69925 


71488 


23 


64790 76173 


66109; 75o3o 


67409 


73865 


68688 


72677 


69946 


71468 


37 


24 


64812' 76154 


66i3i| 75011 


67430 


73846 


6S709 


72657 


69966 


71447 


36 


s5 


64834 76135 


661 53; 74992 


67452 


73826 


6S730 


72637 


69987 


71427 


35 


26 


64856 76116 


66175, 74973 


67473 


73806 


68751 


726n 


i 70008 


71407 


34 


27 


64878. 76097 


661971 74953 


67495 


-3787 


68772 


72597 


70029 


71386 


33 


28 


64901 ' 76078' 66218. 74934, 


67516 


73767 


68793 


72577 


70049 


71366 


32 


29 


64923 76059 66240, 74915, 


67538 


73747 


68814 


72557 


70070 


71343 


3i 


3o 


64945 76041, 


66262, 74896, 


67559 


73728, 


68835 


72537 


70091 


7i325j 3oi 


3i 


64967' 76022 


66284 74876 


67580 


73708 


68857 


72517 


70112 


7i3o5 


29I 
28 1 


32 


64989 76003 


663o6| 74857: 


6760? 


73688: 


68878 


72497 


7oi32 


71284 


33 


65oii 75984 


66327I 74838." 


67623 


73669! 


68899 


72477 


701 53 


71264 


27 


34 


65o33 75965 


66349 74818 


67645 


73649' 


68920 


72457 


70174 


71243 


26 


35 


65o55 75946 


66371, 74799: 


67666 


73629 


68941 


72437 


70193 


71223 


25 


36 


65o77 75927 


66393 74780, 


67688 


73610, 


68c62 


72417 


70215 


71203 


24 


?Z 


65o99 73908 


66414 74-60. 


67709 


73590; 


68983 


72397 


70236 


71182 


23 


38 


63122 75S89 


66436 74741 


67730 


73370 


69004 


72377 


70257 


71162 


22 


39 


65i44 75870 


66458 74722j 


67752 


73551, 


69025 


72357 


70277 


71141 


21 


40 


65 1 66 75831 


66480 74703 j 


67773 


73531 


69046 


72337 


70298 


71121 


20 


41 • 


65i88 75832 


66301: 74683; 


67795 


735: 1 1 


69067 


72317 


70319 


71100 


19 


42 


65210 75Si3 


66523 74664' 


67816 


73491! 


69088 


72297I 


70339 


71080 


18 


43 


65232 75794 


66545 74644 


67S37 


734721 


69109' 72277! 


7o36o 


71059 


17 


44 


65234 75775 


66566 74625, 


67859 


73452' 


69130 


72257 


7o38i 


71039, 


l5 


45 


65276 75756 


665S8j 74606 


67880 


73432 


69i5i 


72236 


70401 


71019 


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66610I 745861 


67901 


73412! 


69172 


72216 


70422 


70998 


14! 


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65320 75719 


66632 745671 


67923 


73393 


69193, 721961 


70443 


70978 


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65342 75699 


66653 74548 


67944 


73373 


692141 72176 


70463 


70957 


12^ 


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66675, 74528 


67965 


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692351 72i56j 


70484 


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66697; 74509 


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73333: 


69256 72i36i 


7o5o5 


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66718, 74489! 


73314: 


69277 721 i6j 


7o525 


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66740' 74470 


68029' 


73294 


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72093 


70546 


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81 


53 


65452 75604 


66762, 74451 


68o5i, 


73274 


69319 


72075| 


70567 


7o855i 


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54 65474 755^5 


66783 74431 


68072 


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668o5] 74412; 


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70608 


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57 


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66848 74373; 


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73.95 


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31 


58 65562 75509 


66870 74353 1 


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73i55 


69445 


71954 


70690' 


70731 


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60 • 656o6 75471: 


66913: 74314 

C.-S. 1 s. 
43 Deg. 1 


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C. S. 1 


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32 


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1 










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Dep. 


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894 


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Dep. 


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831 Deg. 


89t 


Deg. 



TKAVEliSE TAHLE. 



73 



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1 ^ r)eg. 

i 


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Dep. 

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Lat. 
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g 

c 

5 


89^ Deg. 



74 



TRAVI RSE TAKLE 



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1 


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1 

1| i 


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3 


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1.00 


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32.99 0.R6 32.98 


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33 


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33.99 


0.74 


33. 9d U.99 33.98 


1.04 


34 


35 31.99 


0.61 


34.99 


0.76 


'34.99 0.92 34.98 


1.07 


35 


36 '■ ?o . 99 


0.63 


35.99 


0.79 


35.99 , 0.94 35.98 


1.10 


36 


37 36.99 


0.65 


36.99 


O.Sl 


36.99 


' 0.97 36.98 


].13 


37 


3S 


37.99 


0.66 


37.99 


0.83 


37.99 


1 0.99 37.98 


1.16 


33 


39 


3S.99 


0.68 


38.99 


0.85 


38.99 


1 1.0-i 33.98 


1.19 39 


40 


39.99 


0.70 


; 39.99 


0.87 


39.99 


1 1.05 39.93 


^ . 22 40 


41 


40.09 


0.72 


40.99 


0.S9 


40;99 


1.07 40.93 


1 25 41 


42 


41.99 


0.73 


41.99 


, 0.92 


41.99 


1.10 41.93 


1 20 42 


43 


42.99 


0.75 


42.99 


; 0.94 


42.99 


1.13 42.93 i 


I. 31 43 


44 


43.99 


0.77 


43.99 


: 0.96 


43.99 


1.15 43.93 1 


l.o4 14 


45 44.99 


0.79 


44.99 


0.98 


44.99 


1.13 44.98 


1.37 45 


46 45.99 


0.80 


45.99 


' 1.00 


45 . 99 


1.20 45.98 


1.40 46 


47 46.99 


0.82 


46.99 


; 1.03 


46.99 


1.23 46.98 


1.44 47 


4S 47.99 


0.84 


47.99 


, 1.05 


47.98 


1.26 47.93 


1.47 43 


49 4S 99 


0.86 


48.99 


1.07 


48.98 


: 1.28 48.98 


1 . 50 49 1 


50 49 99^ 


0.87 
Lat. 


49.99 


1.09 


49.93 


1 1.31 


, 49.98 
j" Dep. 


l.c3 


i 50 1 


1 


Dep. 


Dep. 


Lat. 


, Dep. 


, Lat 


Lat. 


if 


89] 


Deg. 


88? Deg. 


1 88| Deg. !' 88J 


Deg. 


1 
2 



TRAVERSE TABLE 



75 



5 

w 

p 

'51 


1 

1 Deg. 1 

1 


n Dog. 


1 H Deg. 


1| Deg. 






?• 

'5T 


Lat. 

'50^99 


Dep. 

0.89 


Lat. 


Dep. 

'ITn 


Lat. 


Dep. 


Lat. 

.50.98 


Dep. 


1^079"8" 


1.34 


1.56 


52 


51 99 


0.91 


51.99 


1.13 


51.98 


1.36 


51.98 


1.59 


52 


53 


52 99 


. 92 i 


52.99 


1.16 


52.98 


1.39 


52.98 


1.62 


53 


54 


53 99 


0.94 


.53.99 


1.18 


53.98 


1.41 


53.97 


1.65 


51 


55 


54 99 


0.96 


.54.9- 


1.20 


54.98 


1.44 


.54.97 


1.68 551 


5(5 


5.3.99 


0.98 


55.99 


1.22 


55.98 


1.47 


55.97 


1.71 56 1 


57 


56.99 


0.99 


56.99 


1.24 


56 98 


1.49 


56.97 


1.74 


57 


58 


57.99 


1.01 


57.99 


1.27 


57.9.8 


l.,52 


57.97 


1.77 


58 


59 


58.99 


1.03 


58 . 99 


1.29 


58.98 


1.54 


58.97 


1.80 


59 


60 
61 


59.99 
60.99 


1.05 
LOG 


59. S9 
60.99 


1.31 
1.3''. 


59.98 


1.67 


59.97 


1.83 


60 
61 


60.93 


1.60 


60.97 


1.86 


62 


61.99 


1.08 


61. P9 


1.35 


61. 9S 


1.02 


61.97 


1.89 


62 


63 


62.99 


1.10 


62.99 


1.37 


62. &8 


1.65 


62.97 


1.92 


63 


64 


63.99 


1.12 


63.98 


1.40 


63.93 


1.68 


63.97 


1,95 641 


65 


64.99 


1.13 


64.98 


1.42 


64.08 


1.70 


64.97 


1 99 : 65 ! 


66 


65.99 


1.15 


65.98 


1.44 


85.98 


1.73 


65.97 


2 02 


66 


67 


66.99 


1.17 


66.98 


1.46 


66.98 


1.75 


66.97 


2.05 


67 


68 


67.99 


1.19 


67.98 


1.48 


67.98 


1.78 


67.97 


2.08 


68 


69 


68.99 


1.20 


68.98 


1.51 


68.98 


1.81 


6S 97 


2.11 


C9 


70 

tT 


69.99 
70.99 


1.22 
1.24 


69.98 


1..53 


69.98 


1.83 


69 97 


2.14 
2 ]7 


70 
71 


70.98 


1.55 


70.98 


1.86 


70. 'j7 


72 


71.99 


1.26 


71.98 


1.57 


71.98 


1.88 


71.97 


2.20 


72 


73 


72.99 


1.27 


72.93 


1.59 


72.97 


1.91 


72.97 


2.23 


73 


74 


73.99 


1.29 


73.98 


1.61 


73.97 


1.94 


73.97 


2.26 


74 


75 


74.99 


1.31 


74.98 


1.64 


74.97 


1.96 i 


74.97 


2.29 


75 


76 


75.99 


1.33 


75,98 


1.66 


75.97 


1.99 


75.96 


2.32 


76 


77 


76.99 


1.34 


76.98 


1.68 


76.97 


2.02 


76.96 


2.35 


77 


78 


77.99 


1.36 


77.98 


1.70 


77.97 


2.04 


77.96 


2.38 


78 


79 


78,99 


1.38 


78.98 


1.72 


78.97 


2.07 


78.96 


2.41 


79 


80 


79.99 


1.40 


79.98. 


1.75 


79.97 


2.09 


79.96 


2.44 


80 


81 


80.99"" 


1.41 


80.98 


1.77 


80.97 


2.12 


80.96 


2.47 


'81 


82 


81.99 


1.43 


81.98 


1.79 


81.97 


2.15 


81.96 


2.. 50 


82 


83 


82.99 


1.45 


82.98 


1.81 


82.97 


2.17 


82.96 


2.. 53 


83 


84 


83.99 


1.47 


83 . 98 


1.83 


83.97 


2.20 


83. 9G 


2.57 


84 


85 


84.99 


1.48 


84.98 


1.S5 


84.97 


2.23 


84.96 


2. CO 


85 


86 


85.99 


1.50 


85.98 


1.88 


85.97 


2! 25 


85.96 


2.63 


86 


87 


86.99 


1..52 


86.98 


1.90 


86.97 


2.28 


86.96 


2.66 


87 


88 


87.99 


1.54 


87.98 


1.92 


87.97 


2.30 


87.96 


2.69 


88 


89 


88.99 


1.55 


88.98 


1.94 


88.97 


2.33 


88.96 


2.72 


89 


90 
91 


89.99 


1.57 


89.98 
"90:98" 


1.96 
i.99 


89.97 


2.36 


h'9.96 


2.75 
' 2.78 


90 
91 


90.99 


1.59 


90.97 


2.38 


90.96 


92 


91.99 


1.61 


91 98 


2.01 


9i.9r 


2.41 


91.96 


2.81 


92 


93 92.99 


1.62 


92.98 


2.03 


92.9" 


2.13 


92.96 


2.84 


93 


94 93.99 


1.64 


93.98 


2.05 


93.97 


2.46 


93.96 


2.87 


94 


95 94.99 


1.66 


94.98 


2.07 


94.97 


2.49 


94.96 


2.90 


95 


96 95 99 


1.68 


95.98 


■ 2.09 


95.97 


2.51 


95.96 


2.94 


98 


97 


96,99 


1.69 


96.98 


2.12 


96.97 


2.. 54 


96.95 


2.96 


97 


98 


97.99 


1.71 


97.98 


2.14 


97.97 


2.. 57 


97.95 


2.99 


i 9& 


99 


9H.98 


1.73 


98.98 


2.16 


98.97 


2.. 59 


98.95 


3 02 


1 '^'^ 


100 

CO 

Q 


99.98 
Dep. 


1.75 

i Lat. 


99.98 


2.18 
Lat. 


99.97 


2.62 


99.95 


S.O.') 


■100 

i « 


Dep. 


1 Dep 


Lat. 


Dep. 

88i 


I"u.>; 


89 Dejr. 


881 Deg. 


881 


Deg. 


Dec 


1 rt 

iu 



76 



TRAVERSE TARLE. 





2 Deg. 

i 


2i Deg. 


H Deg. 


2| Deg. 


fC 




Lai. 


Dep. 


Lat. 


Dep.j 


Lat. 


Dep 


Lat. 


Dep. 


n 


'T 


1.00 


0.03 


1.00 


0.04 1 


1.00 


0.04 


1.00 


0.05 


"1 


2 2.00 


0.07 


2.00 


0.08' 


2.00 


0.09 


2.00 


0.10 2 


3 , 3.00 


0.10 


3.00 


0.12 


3.00 


0.13 


3.00 


0.14 2 


4 1 4.00 


0.14 


4.00 


0.16 


4.00 


0.17 


4.00 


0.19' 4 


r. .' 5.00 


0.17 


5.00 


0.20 


5.00 


0.22 


4.99 


0.24 5 


6 6.00 


0.21 


6.00 


0.24 


6.99 


0.26 


5.9.^ 


0.29' 6 


7 7.00 


0.24 


6.99 


0.27; 


6.99 


0.31 


6.99 


0.34. 7 


8 7.99 


0.28 I 


7.99 


0.31 i 


7.99 


0.35 


7.99 


0.38 


8 


9 8.99 


0.31 ! 


8.99 


0.3c 1 


8.99 


0.39 


8.99 


0.43 


9 


10 1 9.99 


0.35 i 


9.99 


0.39 


9.99 


0.44 


9.99 


0.48 


lO 


11 ; 10.99 


0.38 


10.99 


0.43; 


10.99 


0.48 


10.99 


0.53 


Ti 


12 ; 11.99 


42 • 


11.99 


0.47: 


11.99 


0..52 


11.99 


0.58 


12 


13 1 12.99 


0.45 1 


12.99 


0.51 i 


12.99 


0..57! 
0.61 ! 


12.99 


0.62 


13 


14 i 13.99 


0.49 : 


13.99 


0..55! 


13.99 


13.98 


0.67 


14 


15 14.99 


0.52! 


14.99 


0.59' 


14.99 


0.65 
0.70 


14.98 


0.72 


15 


16 1 15.99 


0..56! 


15.99 


0.63' 


15.99 


15.98 


0.77 


16 


17 16.99 


0.59' 


16,99 


0.67 


16.98 


0.74 i 


16.98 


0.82 


17 


18 1 17.99 


0.63 1 


17.99 


0.71! 


17.98 


0.79 


17.98 


0.86 


18 


19 1 18.99 


0.66 


18.99 


0.75! 


18.98 


0.83 1! 18.98 


0.91 


19 


20 19.99 


0.70 i 


19.98 


0.79 


19.98 


0.87 


19.98 


0.96 


20 


21 20.99 


0.73 


20.98 


0.82: 


20.98 


' 0.92 


20.98 


1.01 


21 


22 ;21.99 


0.77! 


21.98 


0.86 


21.98 


0.96 


21.97 


1.06 


22 


23 22.99 


0.80 1 


22.98 


0.90' 


22.98 


1.00 


22.97 


1.10 


23 


24 23.99 


0.84 1 


23.98 


0.941 


23.98 


1.05 


'23.97 


1.15 


24 


25 24.98 


0.871 


24.98 


0.93! 


24.98 


1.09 


24.97 


1.20 


25 


26 25.0'^ 


0.91 


25.98 


1.02 1 


25.98 


1.13 


25.97 


1.25 


26 


27 : 26.98 


0.94 


26.98 


1.061 


26.97 


1.18 


26.97 


1.30 


27 


28 ! 27.98 


0.98 


27.98 


1.10 


27.97 


1.22 


.27.97 


1.34 


28 


29 '28.98 


1.01 


28.98 


1.14 


28.97 


1.26 


23.97 


1.39 


29 


30 29.98 


1.05 ! 


29.98 


1.18 


29.97 


1.31 


29.97 


1.44 


30 

31 


31 130.98 


1.08 1 


30.98 


1.22 


30.97 


1.35 


30.96 


1.49 


32 ,31.98 


1.12 


31.98 


1.26 


31.97 


1.40 


31.96 


1..54 


32 


33 32.98 


1.15 


32.97 


1.30 


32.97 


1.44 


32.96 


1.58 


33 


34 33.98 


1.19' 


33.97 


1.33 


33.97 


1.48 


33.96 


1.63 


34 


35 34.98 


1.22 


34.97 


1.37 


34.97 


1.53 


34.96 


1.68 


35 


36 35.98 


1.26 


35.97 


1.41 


35.97 


1.57 


35.96 


1.73 


36 


37 30.98 


1.29 


36.97 


1.45 


36.96 


1.61 


36.96 


1.78 


37 


38 37.93 


1.33 


37.97 


1.49 


37.96 


1.66 


.37.96 


1.82 


38 


39 38.98 


1.36 


38.97 


1.53 


38.96 


1.70 


,38.96 


1.87 


39 


40 139.98 

41 ! 40.98 


1.40 
1.43 


39.97 


1 67 


139.96 


1.75 


,39.95 


1.92 


40 


40.97 


1.61 


40.96 


1.77 


40.95 


1.97 


41 


42 41.97 


1.47 


41.97 


1.65 


41.96 


1.83 


i 41.95 


2.02 


42 


43 42.97 


1.60 


42.97 


1.69 


42.96 


1.88 


1 42 . 95 


2.C6 


43 


44 43.97 


1.54 


43.97 


1.73 


43 . 96 


1.92 


143.95 


2.11 


44 


45 44.97 


1.57 


44.97 


1.77 


44.96 


1.96 


144.95 


2.16 


45 


40 ' 45.97 


1.61 


45.96 


1.81 


45.96 


2.01 


145.95 


2.21 


46 


47 : 46.97 


1.64 


46.96 


1.85 


46.96 


2.05 


; 46.95 


2.25 


47 


48 47.97 


1.68 


147.96 


1.88 


147.95 


2.09 


47.95 


2.30 


iS 


49 48.97 


1.71 


48.96 


1.92 


,48.95 


2.14 


: 48.94 


2.35 


49 


.'iO 


49.97 


1.74 


49.96 


1.96 
Lat. 


49.95 


2.18 


149.94 


2.40 


50 

i 
1 


o 
u 


! Dep 

88] 


Lat. 

Jeg. 


Dep. 


Dep. 
8'^ 


Lat. 
Deg. 


Dep. 


Lat. 


c3 

.2 


' m 


Deg. 


87i 


Deg. 



TIIAVERSE TABLE. 



77 



p 

3 
? 

51 


1 

2Deg. 


1 n Deg. 


li 

1 n 


Deg. 


21 


Deg. 


5 

51 




Lat. 


Dep. 

~n7s' 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

2.45 




50.97 


50.90 


2.00 


.50.95 


2.22 


50.94 




52 


51.97 


J. 81 


51.90 


2.04 


51.95 


2.27 


51.94 


2.50 


! 52 




58 


52.97 


1.85 


52.96 


2. OS 


.52.95 


2.3] 


52.94 


2.. 54 


i 53 




51 53.97 


1.88 


53.96 


2.12 


53.95 


2.36 


1 53.94 


2.59 


C4 




^5 ' 54.97 


1.92 


54.96 


2.16 


54.95 


2.40 


54.94 


2,64 


55 




56 55 . 97 


1.95 


55.96 


2.20 


55.95 


2.44 


55.94 


2 69 


56 




57 150.97 


1.99 


56.98 


2.24 


56.95 


2.49 


56.93 


2.73 


1 57 




5S 157.96 


2.02 


57.96 


2.28 


57.94 


2.. 53 


.57.93 


2.78 


58 




59 ! 58.98 


2.06 


58.95 


2.32 


58.94 


2.57 


58.93 


2.83 


59 




Gl 


59.98 


2.09 


59 . 95 


2.30 


59 . 94 
60.94 


2.62 
2.66 


59.93 


2.88 


60 




60.90 


2.13 


60,95 


2.39 


60.93 


2.93 




62 


61.90 


2.16 


61.95 


2.43 


61.94 


2.70 


61.93 


2.97 


62 




63 


62.98 


2.20 


62.95 


2.47 


62.94 


2.75 


62.93 


3.02 


63 




64 


63.98 


2.23 


63.95 


2.51 


63.94 


2.79 


63.93 


3.07 


64 




65 


64.96 


2.27 


64.9.7 


2.55 


64.94 


2.84 


64.93 


3.12 


65 




66 


65.93 


2.30 


65.95 


2.. 59 


65.94 


2.83 


65.92 


3.17 


66 




67 


66.96 1 2.34 


00.95 


2.63 


60.94 


2.92 


66.92 


3.21 


67 




63 


67.98 1 2.37 


67.95 


2.67 


67.94 


2.97 


67.92 


3.20 


68 




69 


68.98 


2.41 


68.95 


2.71 


68.93 


3.01 


68.92 


3.31 


69 




70 
71 


69.96 


2.44 


69.95 


2.75 


69.93 


3.05 


89.92 
70.92 


3.30 
3.41 


70 
71 




70.96 


2.48 


70.95 


2.79 


70.93 


3.10 




72 


71.96 


2.51 


71.94 


2.83 


71.93 


3.14 


71.92 


3.45 


72 




73 


72.96 


2.. 55 


72.94 


2.87 


72.93 


3.18 


72.92 


3.. 50 


73 




74 


73.95 


2.58 


73.94 


2.91 


73.93 


3.23 


73.91 


3.55 


74 




75 


74.95 


2.63 


74.94 


2.94 


74.93 


3.27 


74.91 


3.60 


75 




76 


75.95 


2.65 


75.94 


2.98 


75.93 


3.31 


75.91 


3.65 


76 




77 


76.95 


2.69 


76.94 


3.02 


76.93 


3.36 


76.91 


3.70 


77 




78 


77.05 


2.72 


77.94 


3.00 


77.93 


3.40 


77.9) 


3.74 


78 




79 


78.95 


2.76 


78.94 


3.10 


78.92 


3.45 


78.91 


3.79 


79 




80 


79.95 


2.79 


79.94 


3.14 


79.92 


3.49 


79.91 


3.84 


80 




81 


80.95 


2.83 


80.94 


3.18 


80.92 


3.53 


80.91 


3.89 


81 




82 


81.95 


2.86 


81.94 


3.22 


81.92 


3.58 


81.91 


3.93 


82 




83 


82.95 


2.90 


82.94 


3.26 


82.92 


3.62 


82.90 


3.98 


83 




84 


83.95 


2.93 


83.94 


3.30 


83.92 


3.66 


83.90 


4.03 


84 




85 


84.95 


2.97 


84.93 


3.34 


84.92 


3.71 


84.90 


4.08 


85 




86 


85.95 


3.00 


85.93 


3.38 


85.92 


3.75 


8,s 9^ 


4.13 


86 




87 


86.95 


3.04 


86.93 


3.42 


86.92 


3.79 


86.90 


4.17 


87 




88 


87.95 


3.07 


87.93 


3.45 


87.92 


3.84 


87.90 


4.22 


88 




89 


88.95 


3.11 


88.93 


3.49 


88.92 


3.88 


88.90 


4.27 


89 




90 


89.95 


3.14 


89.93 


3.53 


89.91 


3.93 


89.90 


4.32 1 


90 




91 


90.95 


3.18 


90.93 


3.57 


90.91 


3.97 


90.90 


4.37 1 


91 




92 


91.94 


3.21 


91.93 


3.61 


91.91 


4.01 


91.89 


4.41 


92 




93 92.94 1 


3.25 


92.93 


3.65 


92.91 


4.06 


92.89 


4.46 


93 




94 


93.94 


3.28 


93.93 


3.69 


93.91 


4.10 


93.89 


4.51 


94 




95 


94.94 


3.32 


94.93 


3.73 


94.91 


4.14 


94.89 


4.56 


95 




96 


95.94 


3 35 


95.93 


3.77 


95.91 


4.19 


95.89 


4.61 


98 




97 


96.94 


3.39 


96.93 


3.81 


96.91 


4.23 


90.89 


4.65 


97 




98 


97.94 


3.42 f 


97.92 


3.85 


97.91 


4.27 


97.89 


4.7V 


93 




99 


98.94 


3.. 46 


98.92 


3.89 


98.91 


4.32 


98.89 


4.75 


99 




100 

o 

a 


99.94 


3.49 


99.92 


3.93 


99.91 


4.36 


99.88 


_4.8_0_ 
Lat. 


100 

8 

Q 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




88 Deg. 


87| Deg. 


- - 

8711 


3eg. 


87i Deg. 





78 



TRAVERSK TABLE. 



3 
o 
p 


3 Deg. 3i Deg. 


3i Deg. 


3^ Deg. 


a 

' I 


Lat. 


Dep. Lat. 


Dep. 


Lat. 1 Dep. 


Lat. 

1.00 


Dep. 
06 


1.00 


0.05 ! 1.00 


~"o:o6" 


1.00 i .06 


2 


2.00 


0.10 


2.00 


0.11 


2.00' 0.12 


2.00 


-.3 


2 


3 


3.00 


0.16 


3.00 


0.17 


2.99: 0.18 


2.99 


^.iO 


3 


4 


3.99 


0.21 


3.99 


0.23 


3.99 


0.24 


3.99 


0.26 


1 


5 


4.99 


0.26 


4.99 


0.28 


4.99 


0.31 


4.99 


0.33 


5 


6 


5.99 


0.31 


5.99 


0.34 


5.99 


0.37 


5.99 


0.39 


o 


7 


6.99 


0.37 


6.99 


. 40 


6.99 


0.43 
0.49 


6.99 


0.46 


"t 


8 


7.99 


0.42 


7.99 


0.45 


7.99 


7.98 


0.52 


s 


9 


8.99 


0.47 


8.99 


0.51 


8.93 


0..55 


8.98 


O.r/J 


9 


10 
11 


9.99 


0.52 


9.93 


0.57 


9.98 


0.61 


9 98 


. 65 


11 


10.98 


0.58 


10.98 


0.02 


10.98 


0.67 


10". 98 


~0?f2" 


12 


11.98 


0.63 


11.98 


0.68 


11.98 


0.73 


11.97 


0.7S 


12 


13 


12.98 


0.68 


12.93 


0.73 


12.98 


0.79 


12.97 


0.85 


13 


14 


13.98 


0.73 


13.93 


0.79 


13.97 


0.85 


13.97 


0.92 


14 


I.=i 14.98 


0.79 


14.93 


0.85 


14.97 


0.92 


14.9? 


0.98 


15 


16 15. 9S 


0.84 


15.97 


0.91 


15.97 


0.98 


15.97 


1.05 


16 


17 16.98 


0.89 


16.97 


0.96 


16.97 


1.04 


16.96 


l.ll 


17 


IS 


17.98 


0.94 


17.97 


1.02 


17.97 


1.10 


17.96 


1.18 


18 


19 


18.98 


0.99 


18.97 


1.08 


' 18.96 


1.16 1 


18.90 


1.24 


19 


20 
21 


19.97 


1.05 


19.97 


1.13 


i 19.96 


1.22 


19.96 


1.31 


_20 
21 


20.97 


1.10 


20.97 


1.19 


120.96 


1.28 


20 . 96 


1.37 


22 


21.97 


1.15 


21.96 


1.25 


21.96 


1.34 


21.95 


1.44 


22 


23 


22.97 


1.20 


22.96 


1.30 


22.96 


1.40 


22.95 


1.50 


23 


24 


23.97 


1.26 


23.96 


1.36 


23.96 


1.47 


23.95 


1.57 


24 


25 


24.97 


1.31 


24.96 


1.42 


24.95 


1.53 


24.95 


1.64 


25 


26 


25.96 


1.36 


25.96 


1.47 


25.95 


1.59 


25.94 


1.70 


26 


27 


26.96 


1.41 


26.96 


1.53 


26.95 


1.65 


20.94 


1.77 


27 


28 


27.96 


1.47 


27.95 


1.59 


27.95 


1.71 


27.94 


1.83 


28 


29 


23.96 


1..52 


23.95 


1.04 


28.95 


1.77 1 


28.94 


1.90 


29 


39 
31 


29.96 


1.57 


29.95 


1.70 : 

1.76| 


29.94 


l.S3i 


29.94 


1.96 


JO 
31 


30.96 


1.62 


30.95 


30.94 


1.89 


30.93 


2.03 


32 


31.96 


1.67 


31.95 


1.81 


31.94 


1.95 


31.93 


2.09 


32 


33 


32.95 


1.73 


.32.95 


1.87 


32.94 


2.01 


32.93 


2.16 


33 


34 


33.95 


1.78 


33.95 


1.93 1 


33.94 


2.08 


33.93 


2 . 22 


34 


35 


34.95 


1.83 


34.94 


1.93 ' 


34.93 


2.U 


34.92 


2.29 


35 


36 


35.95 


1.88 


35.94 


2.04 i 


35.93 


2.20 


35.92 


2.35 


36 


37 


36.95 


1.94 


36.94 


2.10i 


36.93 


2.26 


36.92 


2.42 


37 


33 


37.95 


1.99 


37.94 


2.15 . 


37.93 


2.32 


37 . 92 


2.49 


38 


39 


33.95 


2.04 


.33.94 


2.21 


38.93 


2.38 1 


33.92 


2.55 


39 


40 


39.95 


2.09 


39.94 


2.27 


39 . 93 


2.44 


39.91 


2.62 


40 


41 


40.94 


2.15 


40.93 


2.32 


40.92 ~~2~,~b0 


40.91 


2 . 68 


"41 


42 


41.94 


2.20 


4U93 


-2. .38 \ 


41-92 


2.56 


41.91 


2.75 


42 


43 


42.94 


2.25 


42 . 93 


2.44 1 


42.92 


2.63 


42.91 


2.81 


43 


44 


43.94 


2 . 30 


43.93 


2.49 j| 43.92 


2.69! 


43.91 


2.88 


44 


45 


44.94 


2.36 


44.93 


2.55 |i 44.92 


2.75 i 


44.90 


2.94 


45 


46 


45.94 


2.41 


45 . 93 


2.61 i 45.91 


2.81 1 


^5.90 


3.01 


JG 


47 


46.94 


2.48 


46.92 


2.66 ;l 46.91 


2.87 i 


46.90 


3.07 


4? 


48 


47.93 


2.51 


47.92 


2.72 1 47.91 


2.93 i 


47.90 


3.14 


48 


49 


48.93 


2.56 


48.92 


2.78 n 48.91 


2.99 ; 


48 . 90 


3.20 


19 


50 

o 
o 

c 

.2 
Q 


49.93 
Dep. 


2.62 
Lat. 


49.92 


2.83 '149.91 


3.05 


49^ 


3.2-7 
Lat. 

Deg. 


50 

h 
1 


Dep. 


L.t. 


Dep. 


Lat. 


Dep. 
80i 


87 E 


>cg. 


86^ 


Deg. 

1 


;;6| Deg. 



TRAVERSE TABLE. 



79 



p 


3 Deg. 


3i Deg. 


1 . 


Deg. 
Dep. ^ 


21 Deg. . 



§ 
51 


Lat 


Dep. 
i 2.G7 


Lat. 


Dep. 


Lat. 


Lat. 


Dep. 
3.34 


61 "50; 93 


'50.92 


2.89 


50.90 


3-11' 


50.89 


fi2 51.93 


i 2.72 


;oJ.92 


2.95 


51.90 


3.17! 


51.89 


3.40 


52 


5S 52.93 


2.77 


li'2.91 


3.00 


52.90 


3.24 


52.89 


3.47 


53 


54 53.93 


2.83 


!.53.91 


3.06 


53.90 


3.30 


53.88 


3.53 


64 


55 5-4.92 


2.88 


54.91 


3.12 


54.90 


3.36 il 54.88 


3.60 


65 


6C 55.92 


2.93 


155.91 


3.17 


.55.90 


3.42:155.88 


3.66 


56 


57 5fi.92 


2.98 


6G.91 


3.23 


56.89 


3.48 56.88 


3 73 


57 


5S 57.92 


3.04 


57.91 


3.29 


57.89 


3.54:! 57.88 


3.79 


58 


59 58.92 


3.09 


58.91 


3.34 


58.89 


3.60 58.87 


3.86 


59 


60 


59.92 


3.14 


; 59.90 
60.90 


3.40 
3.46 


59.89 


3.66 1 


.59.87 
60.87 


3.92 
3.99 


60 
6] 


61 


6U.92 


3.19 


60.89 


3.72' 


62 


6 J. 92 


3.24 


;61.90 


3.51 


61.88 


3.79 i 


61.87 


4.05 


62 


63 


62.91 


3.. 30 


,62.90 


3.57 


,62.88 


3.85i 


62.87 


4.12 


63 


64 


63.91 


3.35 


63.90 


3.63 


! 63.88 


3.91 ! 


63.86 


4.19 


64 


65 


04.91 


3.40 


64.90 


3.69 


; 64.88 


3.97! 


64.66 


4.25 


65 


6G 


65.91 


3.45 


65.89 


3.74 


65.88 


4.03 1 


65.86 


4.. 32 


66 


07 


66.91 


3.51 


66-. 89 


3.80 


,66.88 


4 .09 i 


66.86 


4.38 


67 


68 


67.91 


3.. 56 


67.89 


3.86 


1 67.87 


4.15, 


67.85 


4.45 


68 


69 


68.91 


3.61 


68.89 


3.91 


168.87 


4.211 


68.85 


4.51 


69 


70 
71 


69.90 
70.90 


3.66 


69.89 


3.97 


; 69.87 
170.87 


4.271 
4.33! 


69.85 


4.58 


70 
71 


3.72 


70.89 


4.03 


70.85 


4.64 


72 


71.90 


3.77 


71.88 


4.08 


,71.87 


4.40; 


71.85 


4.71 


72 


73 


72.90 


3.82 


72.88 


4.14 


72.86 


4.46 1 


72.84 


4.77 


73 


74 


73.90 


3.87, 


73.88 


4.20 73.86 


4. .52 1 


73.84 


4.84 


74 


75 


74.90 


3.93 


74.88 


4.25 


74.86 


4.58 


74.84 


4.91 


75 


76 


75.90 


3.98 


75.88 


4.31 


75 86 


4.64 


75.84 


4,97 


76 


77 


76.89 


4.03 


76.88 


4.37 


76.86 


4.70 


76.84 


5.04 


77 


78 


77.89 


4.08 j 


77.87 


4.42 


77 85 


4.76 


77.83 


5.10 


78 


79 


78.89 


4.131 


78.87 


4.48 


78.85 


4.82 


78.83 


5.17 


79 


80 


79.89 


4.19! 


79.87 


4.54' 


r9.85 


4.88 


79.83 


5.23 


80 


81 


80.89 


4.24 1 


80.87 


4. .59 1 


80.85 


4.94 


80.83 


5.30 


81 


82 


81.89 


4.29; 


81.87 


4.66 


81.85 


5.01 


81.82 


5.36 


82 


83 


82.89 


4.341 


82.87 


4.71 


82.85 


5.07 


82.82 


5 43 


83 


84 


83.88 


4.40 


83.86 


4 76 


83.84 


5.13 


83.82 


6.49 


84 


85 


84.88 


4.45 


84.86 


4.82 


'84.84 


5.19 


84.82 


5.56 


85 


86 


85.88 


4.. 50 


85.86 


4 88 


85.84 


5.25 


85.82 


6.62 


86 


87 


86.88 


4..55i 


86.86 


4.93 


86.84 


5.31 


86.81 


5.69 


87 


88 


87.88 


4.61: 


87.86 


4.99 


87.84 


5.37 


87.81 


5.76 


88 


89 


88.88 


4.66 


88.86 


5.05 


88.83 


5.43 


88.81 


6.82 


89 


90 


89.88 


4.71 : 


89.86 


5.10 


89.83 


5.49 


89.81 


5.89 


90 


91 


90.88 


4.76; 


90.85 


5.16 


90.83 


5.56 


90.81 


6.95 


91 


92 


91.87 


4.81 


91.85 


5.22 


91.83 


5.62 


91.80 


6.02 


92 


93 


92.87 


4.87 


92.85 


5.27 


92.83 


5.68 


92.80 


6.08 


93 


94 


93.87 


4.92 1 


93.8.5 


5.33 ; 93.82 


5.74 


93.80 


6.15 


94 


9c 


94. 8r 


4.97 i 


94.85 


5.39:194.82 


6.80 


94.80 


6.21 


95 


96 


95.87 


5.02; 


95.85 


5.4-/ 1195.82 


6.86 


95.70 


6.28 


96 


97 


90.87 


5.08; 


96.84 


5 :(» 


96.82 


5.92 


96.79 


6.34 


97 


98 '97.87 


5.13i 


97.84 


5..'>6 


97.82 


5.98 


97.79 


6.41 


93 


99 98.86 


5.18| 


98.84 


5.61 : 


98.82 


6.04 


98.79 


6.47 


99 


100 
Q 


^9.86^ 
Dep. 


5.23 
Lat. 


99.84 


5.67 1 


99.81 


6.10 


99.79 


6.54 


100 

i 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


8,1 


^eg. 


86| 


Deg. 


83i 


1 
Deg. 


86i Deg. 



80 



TRAvrrsr tattle. 



p 

3 
o 


4 Deg. ' 
1 


4^ Deg. 


H Deg. • 

1 
1 


41 Deg. 
Lat. ■ Dep. 


E' 

a 
a 
a 


Lat. 


Dep. 1 


Lat. 


Dep. 


Lat. 


Dep. 


~1 


"TToo" 


0.07 i 


1.00 


0.07 


1.00 


0.08 


1.00 


0.08 


i 


2 2.00 


0.14 


1.99 


0.15 


1.99 


16 ! 


1.99 


0.17 


s 


3| 2.99 


0.21 ! 


2.99 


0.22: 


2.99 


24 1 


2.99 


0.25 


3 


4 1 a 99 1 


0.28 


3.99 


0.30 1 


3.99 


31 1 


3.98 


0.23 


1 


5 4. 99 1 


0.35 


4.99 


0.37 


4.98 


0.39 1 


4.98 


0.41 


5 


6 , 5.99, 


0.42 


5.98 


0.44 


5.98 


0.47 


5.98 


0.50 


5 


7 


6.98 


0.49 


6.98 


0.52 


6.98 


0..55 


6.97 


0.5S 


7 


8 


7.98 


0.56 


7.98 


0.59 


7.98 


0.63 


7.97 


0.06 


8 


9 


8.98 


0.63 


8.98 


0.67 


8.97 


0.71 


8.97 


0.75 


9 


10 1 


9.98 


0.70 


9.97 


0.74 


9.97 


0.78 


9.97 


0.83 


10 


Hi 


10.97 


0.77 


10.97 


0.82 


10.97 


0.86 


10.96 


0.91 


ii 


12 1 


11.97 


0.84 


11.97 


0.89 


11.96 


0.94 


11.96 


0.99 


12 


13 1 


12.97 


0.91 


12.96 


0.96 


12.96 


1.02 


12.96 


1.08 


J3 


14 


13.97 


0.98 


13.96 


1.C4 


13.96 


1.10 


13.95 


1.16 


14 


15 


14.96 


1.05 


14.96 


1.11 


14.95 


1.18 


14.95 


1.24 


15 


16 


15.96 


1.12 


15.96 


1.19 


15.95 


1.26 


15.95 


1.32 


16 


17 


16.96 


1.19 


16.95 


1.26 


16.95 


1.33 


16.94 


1.41 


17 


18 1 


17.96 


1.26 


17.95 


1.33 


17.94 


1.41 


17.94 


1.49 


18 


19 


18.95 


1.33 


18.95 


1.40 


18.94 


1.49 


18.93 


1..57 


19 


20 

21 


19.95 


1.40 


19.95 


1.48 
1.56 


19.94 


1.57 


19.93 


1.66 


20 
21 


20.95 


1.46 


20.94 


20.94 


1.65 


20.93 


1.74 


22 


21.95 


1.53 


21.94 


1.63 


21.93 


1.73 


21.92 


1.82 


22 


23 


22.94 


1.60 


22.94 


1.70 


22.93 


1.80 


22.92 


1.90 


23 


24 


23.94 


1.67' 


23.93 


1.78 


23.93 


1.88 


23.92 


1.99 


24 


25 


24.94 


1.74 


24.93 


1.85 


24.92 


1.96 


24.91 


2.07 


25 


26 


25.94 


1.81 


25.93 


1.93 


25.92 


2.04 


25.91 


2.15 


26 


27 


20.93 


1.88 


26.93 


2.00 


26.92 


2.12 


26.91 


2.24 


27 


28 


27.93 


1.95 


27.92 


2.08 ' 


27.91 


2.20 


27.90 


2.32 


28 


29 


28.93 


2.02 


28.92 


2.15 


28.91 


2.28 


28.90 


2.40 


29 


30 


29.93 


2.09 


29.92 
30.91 


2.22 


29.91 


2.35 


29.90 


2.48 


30 
'31 


31 30.92 


2.16 


2.30 


30.90 


2.43 


30.89 


2.57 


32 31.92 


2.23 


31.91 


2.37 


31.90 


2.51 


31.89 


2.65 


^12 


33 


32.92 


2.30 


32.91 


2.45 


32.90 


2.69 


32.89 


2.73 


33 


34 


33.92 


2.37 


33.91 


2.52 


33.90 


2.67 


33.88 


2.82 


34 


35 


34.91 


2.44 


34.90 


2.59 


34.89 


2.75 


34.88 


2.90 


35 


36 


35.91 


i 2.51 


35.90 


2.67 


35.89 


2.82 


35.88 


2.98 


36 


37 


36.91 


1 2.58 


36.90 


2.74 


36.89 


2.90 


36.87 


3.06 


37 


38 


37.91 


2.65 


37.90 


2.82 


37.88 


2.98 


37.87 


3.15 


38 


39 


38.90 


2.72 


38.89 


2.89 


38.88 


3.06 


38.87 


3.23 


39 


40 


39.90 


1 2.79 


39.89 


2.96 


39.88 


3.14 


39.86 


3.31 


40 


41 


40.90 


2.86 


40.89 


3.04 


40.87 


3.22 


40.86 


3.40 


"41 


42 


41.90 


2.93 


41.88 


3.11 


41.87 


3.30 


41.86 


3.48 


42 


43 


42.90 


3.00 


42.88 


3.19 


42.87 


3.37 


42.85 


3.56 


43 


44 


43.89 


3.07 


43.88 


3.26 


43.86 


3.45 


43.85 


3.64 


44 


45 


44.89 


1 3.14 


44.88 


3.33 


44.86 


3.53 


44.85 


3.73 


4r. 


46 


45.89 


i 3.21 


45.87 


3.41 


45.se 


3.61 


45.84 


i 3.81 


4G 


47 


46.89 


3.28 


46.87 


3.48 


46.86 


3.69 


46.84 


1 3.89 


4? 


48 


47.88 


3.35 


47.87 


3.56 


47.85 
48.85 


3.77 


47.84 


1 3.97 


1 4^ 


49 


48.88 


8.42 


48.87 


3.63 


3.84 


48.83 


1 4.06 


49 


_60 


49.88 


3.49 


49.86 


3.71 


49.85 


3.92 


49.83 


! 4.14 


50 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 Lat. 


86 


Deg. 


85f Deg. 


851 

1 


Deg. 


85J 


Deg. 


ei 



TRAVERSE TABLE. 



81 



D 

05 
P 

3 
? 

61 


4 Dog. 


4i Deg. 


H Deg. 


4| Deg. 


& 

3 
? 

51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


50. 8S 


3.5G 


50.86 


3.78 


50.84 


4.00 


50.82 


4.22 


o2 


51.87 


3.63 


51.86 


3.85 


51.84 


4.08 


51.82 


4.31 


52 


53 


52.87 


3.70 


52.85 


3.93 


52.84 


4.16 


52.82 


4.39 


53 


51 


53.87 


3.77 


53.85 


4.00 


53.83 


4.24 


53.81 


4.47 


54 


55 


54.87 


3.84 


54.85 


4.08 


54.83 


4.32 


54.81 


4-55 


55 


56 


55.86 


3.91 


55.85 


4.15 


55.83 


4.39 


55.81 


4.64 


56 


57 156.86 


3.98 


56.84 


4.22 


56.82 


4.47 


56.80 


4.72 


57 


58 


57.86 


4.05 


57.84 


4.30 


57.82 


4.55 


57 80 


4.80 


58 


59 


58.86 


4.12 


58.84 


4.37 


58.82 


4.63 


58.80 


4.89 


59 


60 
61 


59.85 


4.19 


59.84 


4.45 


59.82 


4.71 


59.79 


4.97 


60 
61 


60.85 


4.26 


60.83 


4.52 


60.81 


4.79 


60.79 


5.05 


62 


61.85 


4.32 


61.83 


4.59 


61.81 


4.86 


61.79 


5.13 


62 


63 


62.85 


4.39 


62.83 


4.67 


62.81 


4.94 


62.78 


5.22 


63 


64 


63.84 


4.46 


63.82 


4.74 


63.80 


5.02 


63.78 


5.30 


64 


65 


64.84 


4.53 


64.82 


4.82 


64.80 


5.10 


64.78 


5.38 


65 


66 


65.84 


4.60 


65.82 


4.89 


65.80 


5.18 


65.77 


5.47 


66 


67 


66.84 


4.67 


66.82 


4.97 


66.79 


5.26 


66.77 


5.55 


67 


f)8 


67.83 


4.74 


67.81 


5.04 


67.79 


5.34 


67.77 


5.63 


68 


69 


68.83 


4.81 


68.81 


5.11 


68.79 


5.41 


68.76 


5.71 


69 


70 
71 


69.83 


4.88 


69.81 


5.19 


69.78 


5.49 


69.76 


5.80 
5.88 


70 
71 


70.83 


4.95 


70.80 


5.26 


70.78 


5.57 


70.76 


72 


71.82 


5.02 


71.80 


5.34 


71.78 


5.65 


71.75 


5.96 


72 


73 


72.82 


5.09 


72.80 


5.41 


72.77 


5.73 


72.75 


6.04 


73 


74 


73.82 


5.16 


73.80 


5.48 


73.77 


5.81 


73.75 


6.13 


74 


75 


74.82 


5.23 


74.79 


5.56 


74.77 


5.88 


74.74 


6.21 


75 


76 


75.81 


5.30 


75.79 


5.63 


75.77 


5.96 


75.74 


6.29 


76 


77 


76.81 


5.37 


76.79 


5.71 


76.76 


6.04 


76.74 


6.38 


77 


78 


77.81 


5.44 


77.79 


5.78 


77.76 


6.12 


77.73 


6.46 


78 


79 


78.81 


5.51 


78.78 


5.85 


78.76 


6.20 


78.73- 


6.54 


79 


80 
81 


79.81 


5.58 


79.78 
80.78 


5.93 


79.75 


6.28 


79.73 


6.62 


80 
81 


80.80 


5.65 


6.00 


80.75 


6.36 


80.72 


6.71 


82 


81.80 


5.72 


81.78 


6.08 


81.75 


6.43 


81.72 


6.79 


82 


83 


82.80 


5.79 


83.77 


6.15 


82.74 


6.51 


82.71 


6.87 


83 


84 


83.80 


5.86 


83.77 


6.23 


83.74 


6.59 


83.71 


6.96 


84 


85 


84.79 


5.93 


[84.77 


6.30 


84.74 


6.67 


84.71 


7.04 


85 


86 


85.79 


6.00 


85.76 


6.37 


85.73 


6.75 


85.70 


7.12 


86 


87 


86.79 


6.07 


86.76 


6.45 


85.73 


6.83 


86.70 


7.20 


87 


88 


87.79 


6.14 


87.76 


6.52 


87.73 


6.90 


87.70 


7.29 


88 


89 


88.78 


6.21 


88.76 


6.60 


88.73 


6.98 


88.70 


7.37 


89 


90 
91 


89.78 


6.28 


89.75 
90.75 


6.67 


89.72 


7.06 


89.69 


7.45 


90 
91 


90.78 


6.35 


6.74 


90.72 


7.14 


90.69 


7.. 54 


92 


91.78 


6.42 


91.75 


6.82 


91.72 


7.22 


91.68 


7.62 


92 


93 


92.77 


6.49 


92.74 


6.89 


92.71 


7.30 


92.68 


7.70 


93 


94 


93.77 


6.56 


93.74 


6.97 


93.71 


7.38 


93.68 


7.78 


94 


95 


94.77 


6.63 


94.74 


7.04 


94.71 


7.45 


94.67 


7.87 


95 


96 95.77 


6.70 


95.74 


7.11 


95.70 


7.53 


95.67 


7.95 


96 


f)7 196.76 


6.77 


96.73 


7.19 


96.70 


7.61 


96.67 


8.03 


97 


98 


97.76 


6.84 


97.73 


7.28 


97.70 


7.69 


97.66 


8.12 


as 


99 


98.78 


6.91 


98.73 


7.34 


98.69 


7.77 


98.66 


8.20 


99 


100 

0) 


99.76 
Dep. 


6.98 
Lat. 


99.73 


7.41 


39.69 


7.85 


99.66 


8.28 


m 

o 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


.2 


86 I 


3eg. 


1 m 


Deg. 


851 Deg. 


85i 


Deg. 



82 



TRAVERSE TABLE. 



5 

3 
o 
o 


5D 


eg- 


\ 

5i Deg. 


H Deg. 


5} Deg. 1 

1 


C 

p 




Lat. 

"roo 


Dep. 
0.09 


Lat. j 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 




1.00 


0.09 


1.00 


0.10 


0.99 


O.ir' 1 




2 


1.99 


0.17 


1.99 


0.18 


1.99 


0.19 


1 . 99 


O.i;) 2 




3 


2.99 


0.26 


2.99 


0.27 


2.99 


0.29 


2 . 98 


0.30 3 




4 


3.98 


0.35 


3.98 


0.37 


3.98 


0.38 


3.98 


0.40 


4 




5 


4.98 


0.44 


4.98 


0.46 


4.98 


0.48 


4.97 


0..50 


5 




6 


5.98 


0.52 


5.97 


0.55 


5.07 


0.58 


5.97 


0.60 


6 




?( 6.97 


0.61 


0.97 


0.64 


6.97 


0.67 


6.96 


0.70 


7 




8i 7.97 


0.70 


7.97 


0.73 


7.06 


0.76 


7.96 


0.80 


8 




9 8.97 


0.78; 


8.96 


0.82 


8 96 


'0.86 


8.95 


0.90 


9 




10 
11 


9.9o 
10.96 


0.87, 


9.96 


0.92 


9.95 


0.96 


9.95 


1.00 


1^' 
11 




6.96 


10.95 


1.01 


10.95" 


1.05 


10.94 


KIO 




12 


11.95 


1.05 1 


1 1 . 9o 


1.10 1 


1 1 . 94 


1.15 


11.94 


1.20 


12 




13 


12.95 


1.13 1 


12.95 


1.19 


12.94 


1.25 


12.93 


1.30 


13 


14 


13.95 


1.22! 


13.94 


1.28 


13.94 


1.34 


13.93 


1.40 


14 


15 


14.94 


1.31 


14.94 


1.37 


14.93 


1.44 


14.92 


1..50 


15 




16 


15.94 


1.39: 


15.93 


1.46 


15.93 


1.53 


15.92 


1 . 60 


lb 




17 


16.94 


1.48 


16.93 


1.56 


16.92 


1.63 


16.91 


1.70 


17 




18 


17.93 


1.57 


17.92 


1.65 


17.92 


1.73 


17.91 


1.80 


18 




19 


18.93 


1.66 


18.92 


1.74 


18.91 


1.82 


18.90 


1.90 


19 




20 

'21 


19.92 


1.74 


19.92 


1.83 


19.91 
20 . 90 


1.92 


19.90 


2.00 


20 
21 




20.92 


1.83 


20.91 


1.92 


2.01 


20.89 


2.10 1 




22 


21.92 


1.92 


21.91 


2.01 


21.90 


2.11 1 


21.89 


2.20 


22 




23 


22.91 


2.00! 


22.90 


2.10 


22.89 


2'. 20 


22.88 


2.30 


23 




24 


23.91 


2.09 


23.90 


2.20 


23.89 


2.30 


23.88 


2.40 


24 




25 


24.90 


2.18 


24.90 


2.29 


24.88 


2.40 


24.87 


2.50 


25 




26 


25.90 


2.27 


25.89 


2.38 


25.88 


2.49 i 


25.87 


2.60 


26 




27 


26.90 


2.35 


26.89 


2.47 


26.88 


2.59 


26.86 


2.71 


27 




28 


27.89 


2.44 


27.88 


2.56 


27.87 


2.08 


27.86 


2.81 


28 




29 


28.89 


2.53 


28.88 


2.65 


28.87 


2.78 


28.85 


2.91 


29 




30 
31 


29.89 
30.88 


2.61 


29.87 


2.75 


29.86 
30.86 


2.88 
2.97 


29.85 


3.01 


30 




2.70 


30.87 


2.84 


30.84 


3.11 


31 




32 


31.88 


2.79 


31.87 


2.93 


31.85 


3.07 


31.84 


3.21 


2Z 




33 


32.87 


2.88 


32.86 


3.02 


32.85 


3.16 


32.83 


3.31 


33 




34 


33.87 


2.96 


33.86 


3.11 


33.84 


3.26 


33.83 


3.41 


34 




35 


34.87 


3.05 


34.85 


3.20 


34.84 


3.35 


34.82 


3.51 


3.> 




36 


35.86 


3.14 


35.85 


3.29 


35.83 


3.45 


35.82 


3.61 


36- 




37 


36.86 


3.22 


36.84 


3.39 


36.83 


3.55 


36.81 


3.71 


37 




38 


37.86 


3.31 


37.84 


3.48 


37.83 


3.64 


37.81 


3.81 


38 




39 


38.85 


3.40 


38.84 


3.57 


38.82 


3.74 


38.80 


3.91 


39 




40 


39.85 


3.49 


39.83 


3.66 


39.82 


3.83 


39.80 


4.01 


40 




41 


40.84 


3.57 


40.83 


3.75 


40.81 


3.93 


40.79 


4.11 


41 




42 


41.84 


3.66 


41.82 


3.84 


41.81 


4.03 


41.79 


4.21 


42 




43 


42.84 


3.7B 


42.82 


3.93 


42.80 


4.12 


42.78 


4 31 


43 




44 


43.83 


3.83 


43.82 


4.03 


43.80 


4.22 


43.78 


4 il 


44 




45 


44.83 


3.92 


44.81 


4.12 


44.79 


4.31 


44.77 


4 51 


45 




40 


45.82 


4.01 


45.81 


4.21 


45.79 


4.41 


45.77 


4 61 


46 




47 


46.82 


4.10 


46.80 


4.30 


46.78 


4.50 


46.76 


4.71 


47 




48 


47.82 


4.18 


47.80 


4.39 


47.78 


4.60 


47.76 


4.81 


45 




49 


48.81 


4.27 


48,79 


4.48 


48 . 77 


4.70 


48.75 


i 4.91 


49 




fJO 


49.81 


4.36 


49.79 
Dep. 


4.58 
1 ?.at. 


49.77 
Dep. 


4.79 
Lat. 


49 . 75 


5.01 
Lat. 


f 




03 


l>oi>. 


1 Lat. 


Dep. 




85 


Deg. 


84J 


Deg. 


84^ Deg. 


84i Deg. 

1 


'■ 



TRAvEHSE TA±lLE. 



83 



OS 

3 
o 
o 

61 


5Deg. 


5i Deg. 


H 


Deg. 


■n 


Deg. 


i C 

■ 
1 p 

'51 


Lat. 


Dep. 


Lat. 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 
5.11 


50.81 


4.44 |i 50.79 


4.67 


50.77 


4.89 


50 74 


52 


51.80 


4.53 [51.78 


4.76 


'51.76 


4.98 


51 74 


6.21 


52 


53 


52.80 


4.62! 52.78 


4.85 


j 52.76 


5.08 


52 73 


5.31 


5o 


64 


53.79 


4.71 


53.77 


4.94 


' 53.75 


5.18 


53 73 


5.41 


54 


55 


54.79 


4.79 


54.77 


5.03 


54.75 


5.27 


54.72 


5.51 


55 


56 


55.79 


4.88 


55.77 


5.12 


55.74 


5.37 


55.72 


5.61 


56 


57 


56.78 


4.97 


56.76 


5.22 


156.74 


5.46 


56.71 


5.71 


57 


58 


57.78 


5.06 


57.76 


5.31 


J 57.73 


5.56 


57.71 


5.81 . 58 


59 


58.78 


5.14 


58.75 


5.40 


j 58.73 


5.65 


58.70 


5.91 59 


60 
61 


59.77 
60.77 


5.23 
5.32 


59.75 
60.74 


5.49 


159.72 


5.75 


59.70 


6.01 : 60 


5.58 


60.72 


5.85 


60.69 


6.11 , 61 


62 


61.76 


5.40 


61.74 


5.67 


61.71 


5.94 


61.69 


6.21 


62 


63 


62.76 


5.49 


62.74 


5.76 


62.71 


6.04 


62.68 


6.31 


63 


64 


63.76 


5.58 


63.73 


5.86 


63.71 


6.13 


63.68 


6.41 


64 


65 


64.75 


5.67 


64.73 


5.95 


64.70 


6.23 


64.67 


6.51 


65 


66 


65.75 


5.75 


65.72 


6.04 


65.70 


6.33 


65.67 


6.61 


66 


67 


66.75 


5.84 


66.72 


6.13 


66.69 


6.42 


66.66 


6.71 


6? 


68 


67.74 


5.93 


67.71 


6.22 


67.69 


6.52 


67.66 


6.81 


68 


69 


68.74 


6.01 


68.71 


6.31 


68.68 


6.61 


68.65 


6.91 


69 


70 

71 


69.73 


6.10 


69.71 


6.41 


69.68 
70.67 


6.71 
6.81 


69.65 


7.01 


70 


70.73 


6.19 


70.70 


6.50 


70.64 


7.11 


71 


72 


71.73 


6.28 


71.70 


6.59 


71.67 


6.90 


71.64 


7.21 1 72! 


73 


72.72 


6.36 


72.69 


6.68 


72.66 


7.00 


72.63 


7.31 


73 


74 


73.72 


6.45 


73.69 


6.77i 


73.66 


7.09 


73.63 


7.41 


74 


75 


74.71 


6.54 


74.69 


6.86i 


74.65 


f 7.19 


74.62 


7.51 


75 


76 


75.71 


6.62 


75.68 


6.95 


75.65 


7.28 


75.62 


7.61 


76 


77 


76.71 


6.71 


76.68 


7.05 


76.65 


7.38 


76.61 


7.71 


77 


78 


77.70 


6.80 


77.67 


7.14 


77.64 


7.48 


77.61 


7.81 


78 


79 


78.70 


6.89 1 


78.67 


7.23 


78.64 


7.57 


78.60 


7.91 


79 


80 
81 


79.70 


6.97' 


79.66 


7.32 


79.6b 


7.67 


.79.60 


8.02 


80 


80.69 


7.06 '80.66 


7.41 


80.63 


7.76 


80.59 


8.12 


81 


82 


81.69 


7.15 181.66 


7.50 


81.62 


7.86 


81.59 


8.22 


82 


83 


82.68 


7.23 


82.65 


7.59 


82.62 


7.96 


82.58 


8.32 


83 


84 


83.68 


7.32 


83.65 


7.69 


83.61 


8.05 


83.58 


8.42 


84 


85 


84.68 


7.41 


84.64 


7.78 


84.61 


8.15 


84.57 


8.52 


85 


86 


85.67 


7.50 


85.64 


7.87 


85.60 


8.24 


85.57 


8.62 


86 


87 


86.67 


7.58 


86.64 


7.96 


86.60 


8.341 


86.56 


8.72 


87 


88 


87.67 


7.67 


87.63 


8.05 


87.59 


8.43 


87.56 


8.82 


8S 


89 


88.66 


7.76 


88.63 


8.14 


88.59 


8.53! 


83.55 


8.92 


89 


90 
91 


89.66 
90.65 


7.84 
7.93 


89.62 


8.24 


89.59 


8.63! 
8.72 i 


89.55 


9.02 


00 


90.62 


8.33 


90.58 


90.54 


9.12 


91 


92 


91.65 


8.02 


91.61 


8.42 


91.58 


8.82 1 


91.54 


9.22 


92 


93 


92.65 


8.11 


92.61 


8.51 1 


92.57 


8.91 1 


92.53 


9.32 


93 


94 


93.64 


8.19 


93.61 


8.601 


93.57 


9.01 


93.53 


9.42 


94 


95 


94.64 


8.28 


94.60 


8.69! 


94.56 


9.11 1 


94.52 


9.52 


95 


96 


95.63 


8.37 


95.60 


8.78' 


S5.56 


9.20 


95.52 


9.62 


96 


97 


96.63 


8.45 


96.59 


8.88 1 96.55 


9.30 


96.51 


9.72 


97 


98 


97.63 


8.54 


97.59 


8.97 j 97.55 


9.39I 


97.51 


9.82 


98 


99 


98.62 


8 63 


98.59 


9.06 i 93.54 


9.49! 


93.50 


9.92 991 


100 


99.62 


8.72 


99.58 


9.15 1 99.54 


9.58! 


99.50 
"Dep. 


10.02 
Lat 


100 

1 


Dep. 


Lat. 


Dep. 


Lat.| 

! 


Dep. 


Lat.| 


851 


)eg. 


84} Deg. 


84i Deg. 


84J Deg 



20 



84 



TRAV7RSE TA-BLE. 



fa ! 


6 Deg. 


e\ Dcg. 1 

1 


6| Deg. 1 


6a Deg. 


7.' 




Lat. 


Dep. 


Lat. 


Dep. j 


Lat. 

0.99 


Dep. 

o.ui 


Lat. 


Dep. 




C3 


1 I 


0,99 


0.10 ' 


0.99 


0.11 


0.99 


~'07l2"i T 


a ■ 1 99 


0.21 1 


1.99 


0.22 1 


1.99 


0.23 


1.99 


24' 2 


3, 2 9S 


0.31 1 


2.98 


0.33! 


2.93 


0.34; 


2.98 


35 ! 3 


4 ' 3 98 


3.41 ; 


3.93 


44 i 


3.97 


0.45' 


3.97 


0.47 1 4 


5! 4.97 


0.52 


4.97 


-).54i 


4.97 


0.57! 


4.97 


0.59 i 3 


6|. 5.97 


0.63 


5.96 


0.80, 


5.96 


0.63 


5.96 


0.71 : 8 


7 6.96 


0.73 


6.96 


0.76; 


6.96 


0.79 


6.95 


0.82! 7 


8 


7.96 


0.S4 


7.95 i 0.87 j 


7.95 


0.91 1 


7.94 


0.94, S 


9 


8.95 


0.94 


8.95 1 0.93 


8.94 


1.02! 


8.94 


LOG I 9 


10 
11 


9.95 
10.94 


1.05 


9.94! 1.09 i 


9.94 


1.13: 

1.25! 


9.93 
10.92 


1.181 10 
1.29 ' 11 


1.15 


10.93 


1.20 1 


10.93 


12 


11.93 


1.25 


11.93 


1.31 i 


11.92 


1.36] 
1.47! 


11.92 


1.41 12 


13 


12.93 


1.36 


12.92 


1.42 


12.92 


12.91 


1.53; 13 


14 


13.92 


1.46 


13.92 


1.52 


13.91 


1.59 


13.90 


1.60' 14 


15 


14.92 


1.571 


14.91 


1.63 i 


14.90 


1.70! 


14.90 


1.76 15 


16 


15.91 


1.67! 


15.90 


1.74, 


15.90 


1.81 1 


15.89 


1.88 ^ 16 


17 


16.91 


1.78, 


16.90 


1.85 


16.89 


1.92 


16.88 


2 00 1 17 


18 


17.90 


1.88 i 


17.89 


1.96, 


17.88 


2.04 


17.88 


2.12 13 


19 


18.90 


1.99 ' 


18.89 


2.07 


18.83 


2.15 


18.87 


2.23 19 


20 


19.89 


2.09: 


19.88 


2.18 


19.87 


2.26 


19.86 


2.35 


20 


21 


20.88 


2.20' 


20.88 


2.29 


20.87 


2.38 


20.85 


2.47 


21 


22 


21.88 


2.30; 


21.87 


2.40 


21.86 


2.49 


21.85 


2.59 22 


23 


22.37 


2.40 


22.86 


2.50 


22.85 


2.00 


22.84 


2.70 23 


24 


23. S7 


2.51 ! 


23.86 


2.61 


23.85 


2.72 


'23.83 


2.82 . 24 


25 


24.88 


2.61 1 


24.85 


2.72 


24.84 


2.83 


24.83 


2.94 25 


26 


25.86 


2.72 j 


25.85 


2.83 


25.83 


2.94 


25.82 


3.06 26 


27 


26.85 


2.82 


26.84 


2.94 


,26.83 


3.06 


'26.81 


3.17 27 


2S 


27.85 


2.93 


27.83 


3.05 


27.82 


3.17 


.27.81 


3.29 23 


29 


28.84 


3.03 


28.83 


3.16 


28. 81 


3.28 


'28.80 


3.41 ' 29 


30 


29.84 


3.14 
3.24 


29.82 


3.27 


29.81 


3.40 


29.79 


3.53 30 
3.64 31 


'31 


30.83 


30.82 


3.37 


130.80 


3.51 


30.79 


32 


31 82 


3.34 


31.81 


3.48 


31.79 


3.62 


31.78 


3.76 32 


33 


32.82 


3.45 


32.80 


3.59 


i 32.79 


3.74 


32.77 


3.83 1 33 


34 


33.81 


3.55 


33-80 


3.70 


133.78 


3.85 


33.76 


4.00 1 34: 


35 


34.81 


3.66 


34.79 


3.81 


34.78 


3.96 


34.76 


4.11 35 


36 


35.80 


3.76 


35.79 


3.92 


35.77 


4.08 


35.75 


4.23 ! 36 


37 


36.80 


3.87 


,36.78 


4.03 


1 36.76 


4.19 


36.75 


4.35 1 37 


38 


37.79 


3.97 


' 37.77 


4.14 


37.76 


4.30 


37.74 


4.47 : 3S 


39 


38.79 


4.08 


138.77 


4.25 


33.75 


4.41 


38.73 


4.53; 39 


40 


39.78 


4.18 


[39.76 


4.35 


39.74 


4.53 


i39.72 


4.70! 40 


41 


40.78 


4.29 


140.76 


"4 46 


140.74 


4.64 


! 40.72 


4.82 j 41 


42 


41.77 


4.39 


141.75 


4.57 


141.73 


4.76 


'41.71 


4.941 42 


43 


42.76 


4.49 


42.74 


4.68 


i 42.72 


4.87 


42.70 


5.05 1 43 


44 


43.76 


4.60 


43.74 


4.79 


43.72 


4.93 


: 43.70 


5.17 44 


45 


44.75 


4.70 


44.73 


4.90 


44.71 


5.09 


144.69 


5.29 1 45 


46:45.75 


4.81 


45.73 


5.01 


45.70 


5.21 


145.68 


5.41 . 46 


47 


46.74 


4.91 


46.72 


5.12 


46.70 


5.32 


,46.07 


5 52 ; 47 


48 


47.74 


5.02 


47.71 


5.23 


47.69 


5.43 


147.67 


5.64 


43 


49 


43.73 


1 5.12 


48.71 


6.34 


148.69 


5.55 


j 48.06 


5.76 


49 


50_ 


49.73 


! 5.23 


49.70 


5.44 


149.63 


5.66 


149.65 


5.88 


50 
u 


1 
1 


Dcp. 


|Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


84 


Deg. 


831 Deff. 


831 


Deg. 


m 


Deg. 


._ 



















TRAVERSE TABLE. 



85 



5 

ST 


6 Deg. 


6iDeg. 


6^ Deg 


61 Dog. 


§ 

~51 


o 


- 
Lat. 


Dep. 


Lat. 


Dep. 
^5.55| 


J at. 
50.67' 


Dep. 1 
5.77, 


Lat. 


Df^p. 


51 


50.72 1 


5.33 


50.70 


60.65 


~579b' 


52 51.72 


5.44 


51.69 


5.66 i 


51.67 


5.59 


G1.64 


6.n 


52 


53 52.71 


5.. 54 


52.68 


5.77 


.52.66 


6.0JI 


5^.63 


6.2? 


53 


54 53.70 


5.64 


53.68 5.88 1 


53.60 


G.r-i 


53.63 


6.35 


54 


55 


54.70 


5.75 


54.67 5.99! 


54.65 


6.r.3: 


54.62 


6.16 


5£ 


56 


55.69 


5.85 


55.67 6.101 


55.64 


6 341 


55.61 


6..5S 


56 


57 


56.69 


5.96 


56.66 6.21 


56.63 


6.15! 


50.60 


6.70 


57 


58 


57.68 


6. 06 57.66 6.31 1 


57.63 


6.57i 


57.60 


6.82 


58 


59 


58.68 


6.r/j58.65 6.42 


58.62 


6.68! 


58.53 


6.93 


59 


60 


59.67 


6.27:59.641 6.53 


59.61 


6.79 1 


59.68 


7.05 


60 


61 


60.67 


6.38 ; 60.64 


6.64! 


60.61 


6.91 i 


60.58 


7.17 


61 


62 


61.66 


6. 48 ll 61.63 


6.75 


61.60 


7.02 i 


61.57 


7.29 


62 


03 


62.65 


6.59 62.63 


6.86 


02.60 


7.131 


62.56 


7.40 


63 


64 


63.65 


6.69 l! 63.62 


6.97 


63.59 


7.25 


63.56 


Y.52 


64 


65 


64.64 


6.79 ij 64.61 


7.08 


64.58 


7.36 


64.55 


7.64 


65 


66 


65.64 


6.90 


65.611 7-191 


65.58 


7.47 


65.54 


7.76 


66 


67 


66.63 


7.00; 


66.60 7.29 { 


66.57 


7 58 


66.54 


7.88 


67 


68 


67.63 


7.11 I 


67.60 7,40 1 


67.56 


7.70 


67.53 


7.99 


68 


69 


68.62 


7.211 


68.59 


?.51 


68.56 


7.81 


68.62 


8.11 


69 


70 
'71 


69.62 
70.61 


7.32 i 


69.58 


7.62 


69.55 


7.92 


69.51 


8.23 
8.35 


70 

71 


7.42 1 


70.58 


7.73 


70.54 


8.041 


70.51 


72 


71.61 


7.53 


71.57 


7.84 


71.54 


8.15 


71.50 


8.46 


72 


73 


72.60 


7.63 


72.57 


7.95 


72.53 


8.26 


72.49 


8.58 


73 


74 


73.59 


7.74 


73.. 50 


8.06 


73.52 


8.38 


73.49 


8.70 


74 


75 


74.59 


7.84 


74.55 


8.17 


74.52 


8.49 


, 74.48 


8.82 


75 


76 


75.58 


7.94 


75.. 55 


8.27 


75.51 


8.60 


75.47 


8.93 


76 


77 


76.58 


8.05 


76.54 


8.38 


76.51 


8,72 


76.47 


9.05 


77 


78 


77.57 


8.15 


77.. 54 


8.49 


77.50 


8.83 


77.46 


9.17 


78 


79 


78.57 


8.26 


78.53 


8.60 


78.49 


8.94 


78.45 


9.29 


79 


80 

81 


79.56 


8.36 


79.53 
80.52 


8.71 
8.82 


79.49 


9.06 


79.45 


9.40 


80 
81 


80.56 


8.47 


80.48 


9.17 


80.44 


9.52 


82 


81.55 


8.571 


81.51 


8.93 


81.47 


9.28 


81.43 


9.64 


82 


83 


82.55 


8.68; 


82.51 


9.04 


82.47 


9.40 


; 82.42 


9.76 


8? 


84 


83.54 


8.78- 


83.50 


9.14 


83-46 


9.51 


83.42 


9.87 


84 


85 


84.53 


8.88; 


84.50 


9.25 


84.45 


9.62 


84.41 


9.99 


86 


86 


85.53 


8.99 


85.49 


9.36 


85.45 


9.74 


85.40 


10.11 


86 


87 


86.52 


9.09 


86.48 


9.47 


86.44 


9.85 


86.40 


10.23 


87 


88 


87.52 


9.20 


87.48 


9.58 


87.43 


9.96 


87.89 


10.34 


88 


89 


88.51 


9.30 


88.47 


9.69 


88.43 


10.08 


88.38 


10.46 


89 


90 
91 


89.51 


9.41 


89.47 


9.80 


89.42 


10.19 


89.38 
90.37 


10.58 


90 
91 


90.50 


9.51 


90.46 


9.91 


90.42 


10.30 


10.70 


92 


91.50 


9.62 


91.45 


10.02 


91.41 


10.41 


; 91.36 


10.81 


92 


93 


92.49 


9.72 


92.45 


10.12 


92.40 


10.53 


92.3b 


10.93 


93 


94 


93.49 


9.83 


93.44 


10.23 


93.40 


10.64 


1 93.35 


11.05 


94 


95 


94.48 


9.93 


94.44 


10.34 


94.39 


10.75 


: 94.34 


11.17 


95 


96 


95.47 


10.03 


95.43 


10.45 


95.38 


10.87 


95.33 


11.28 


96 


97 


96.47 


10.14 


96.42 


10.56 


96.38 


10.98 


196.33 


11.40 


97 


93 


97.46 


10.24 


97.42 


10.67 


97.37 


11.09 ii 97.32 


? 1 . 52 


98 


99 


98.46 


10.35 


98.41 


10.78 


98.36 


11.21 1198.31 


11.64 


no 


100 


99.45 


10.46 


99.41 


10.89 


99.36 


11.32 l| 99.31 


il.75 


100 

6 

o 


1 Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


841 


)eg. 


83| Deg. 


8^ 


Deg. 


83i 


Deg. 



86 



TRAVERSE TABLE- 



5 

w 
fa 

a 
n 
? 


7Deg. 


n Deg. 


n^ 


Deg 


7.1 Deg. 


o 


Lat. 


Dep. 


Lat. 


D«p. 


Lat. 


Dep. 


Lat. 


Dep. 


~1 


■"0799" 


0.12 


0.99 


0.13 


0.99 


0.13 


0.99 


0.13 


] 


2 


1.99 


0.24 


1.98 


0.25 


1.98 


0.26 


1.98 


0.27 


s 


3 


2.98 


0.37 


2.98 


0.38 


2.97 


0.39 


2.97 


0.40 


s 


4 


3.97 


0.49 


3.97 


0.50 


3.97 


0.52 


3.96 


0.54 4| 


5 


4 96 


0.61 


4.96 


0.63 


4.96 


0.65 


4.95 


0.67 


6 


6 


5.96 


0,73 


5.95 


0.76 


5.95 


0.78 


5.95 


0,81 





7 


6.95 


0.85 


0.94 


0.88 


6.94 


0.91 


6.94 


0.94 


7 


8 


7.94 


0.97 


7.94 


1. 01 


7.93 


1.04 


7.9a 


1.08 


8 


9 


8.93 


1.10 


8.93 


1.11 


8.92 


1.17 


8.92 


1.21 


9 


10 


9.93 
10.92 


1.22 j 
1 . 34 i 


9.92 


1.26 


9.9.1 


1.31 


9.91 


1..35 


10 


10.91 


1.39 


10.91 


1.44 


10.90 


1.48 


-ir 


12 


11.91 


1.46! 


1 1 . 90 


1.51 


11.90 


1.57 


11.89 


1.G2 1 12| 


13 


12. GO 


1.58; 


12.90 


1.64 


12.89 


1.70 


12.88 


1.75 


13, 


14 


13.90 


1.71 


13.89 


1.77 


13.88 


1.83 


13.87 


1.89 


14 


15 


14.89 


1.83 


14.88 


1.89 


14.87 


1.96 


14.86 


2.02 


15 


16 


15.88 


1.95 1 


15.87 


2.02 


15.86 


2.09 


15.85 


2.16 


16 


17 


16.87 


2.07! 


16.86 


2.15 


16.85 


2.22 


16.84 


2.29 


17 


18 


17.87 


2.19| 


17.86 


2.27 


17.85 


2.35 


17.84 


2.43 


18 


19 


18.86 


2.32 1 


18.85 


2.40 


18.84 


2.48 


18.83 


2.56 


19 


20 
21 


19.85 


2.44 
2.56' 


19.84 
20.83 


2.52 
" 2.65 


19.83 


2.61 


19.82 


2.70 


20 
21 


20.84 


20.82 


2.74 


20.81 


2.83 


22 


21.84 


2.68 1 


21.82 


2.78 


21.81 


2.87 


21.80 


2.97 


22 


23 


22.83 


2.80' 


22.82 


2.90 


22.80 


3.00 


22.79 


3.10 


23 


24 


23.82 


2.921 


23.81 


3.03 


23.79 


3.13 


23.78 


3.24 


24 


25 


24.81 


3.05 


24.80 


3.15 


24.79 


3.20 


24.77 


3.37 


25 


26 


25.81 


3.17 


25 . 79 


3.28 


25.78 


3.39 


25.76 


3.51 


26 


27 


26.80 


3.29 


26.78 


3.41 


26.77 


3.52 


26.75 


3.64 


27 


28 


27.79 


3.41 


27.78 


3.53 


27.76 


3.65 


27.74 


3.78 


28 


29 


28.78 


,^ . §3 


28.77 


3.66 


28.75 


3.79 


28.74 


3.91 


29.1 


80 
31 


29.78 


3.06 


29.76 


3.79 


29.74 


3 92 


29.73 
30.72 


4.05 

4.18 


30 


30.77 


3.78 


.30.75 


3.91 


30.73 


4.05 


31 


32 


31.76 


3.90 


31.74 


4.04 


31.73 


4.18 


31.71 


4.32 


32 


33 


32.75 


4.02 


32.74 


4.16 


32.72 


4.31 


32.70 


4.45 


33 


34 


33.75 


4.14 


83.73 


4.29 


33.71 


4.44 


33.69 


4.58 


34 


35 


34.74 


4.27 


34.72 


4.42 


34.70 


4.57 


34.68 


4.72 


35 


36 


35.73 


4.39 


35 .7 1 


4.54 


35.69 


4.70 


35.67 


4.85 


ae 


37 


36.72 


4.51 


36.70 


4.67 


.36.68 


4.83 


36.66 


4.99 


37 


38 


37.72 


4.63 


37.70 


4.80 


37.67 


4.96 


37.65 


5.12 


38 


39 


38.71 


4.75 


38.69 


4.92 


38.67 


5.09 


38.64 


5.26 


39 


40 


39.70 


4.87 


39.68 


5.05 


39.66 


5.22 


39.63 


5.39 


40 


41 


40.70 


5.00 


40.67 


5.17 


40.65 


5.35 


40.63 


6.. 53 


"41" 


42 


41.69 


5.12 


41.66 


5.30 


41.64 


6.48 


41.62 


5.66 


42 


43 


42.68 


5.24 


42.66 


5.43 


42.63 


5.61 


42.61 


5.80 


4» 


44 


43.67 


5.36 


43.65 


5.. 55 


43.62 


5.74 


43.60 


6.93 


44 


45 44 67 


5.48 


44.64 


5.68 


44.62 


6.87 


44.69 


6.07 


45 


46 , 45.66 


5.61 


45.63 


5.81 


45.61 


6.00 


45 68 


6.20 


46 


47 46,65 


5.73 


46.62 


6.93 


46.60 


6.13 


46.57 


6.34 


47 


48 


47.64 


5.85 


47.62 


6.06 


47.59 


6.27 


1 47.56 


6.47 


48 


49 


48 . 63 


5.97 


48.61 


6.18 


48.58 


6.40 


; 48.55 


6.61 


49 


50 


49.63 


6.09 


49.60 


6.31 


49.57 


6.53 


49.54 


6.74 


50 




Dep» 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 
o 


63] 


Deg. 


82| Deg. 


821 


Deg. 


824 Deg. 



TRAVEFcSE TABLE. 



87 



o 

3 
O 

a 
"51 


7Deg. 


n 1 


3eg. 


U Deg. 


7| D6g. 

1 


a 

§ 

'51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

6,83 


50.62 


6.22 


50.59 


6.44 1 


~5f 56" 


0.66' 


50.53 


52 


51.01 


6.34 


51.. 58 


6.56 u 51.56 
6.69^2.55 


6.79 


51.53 


7,01 < 


52 


53 


52.60 


6.46 


52.58 


6.92 1 


52.52! 7.15 


53 


54 


53.60 


6.53 


53.57 


6.81 


53.54 


7,05 1 


53.51 


7.28 


54 


55 


54.59 


6. 70 


54.56 


6.94 


54.53 


7.18i 


54. fO 


7.42 


55 


56 


55.58 


6.82 


i;5.55 


7.07 


55.52 


7 31 


55.49 


7.55 


56 


57 


56.58 


6.95 


56.54 


7.19 


56.51 


7 4-tl 


56.43 


7.69 


57 


53 


57.57 


7.C7 


57.54 


7.32 


57.50 


7.57! 


57.47 


7.82 


53 


59 


5S.56 


7.19 


58.53 


7.45 


53.50 


7.70 1 


58.46 


7.96 


59 


60 
61 


59.55 
60.55 


7.31 


59.52 
60.51 


7.57 1 


59.49 


7.83 1 


59.45 


8.09 


60 

' ei 


7.43 


7.70 


60.48 


7.96 


60.4^4 


8.23 


62 


61.54 


7.56 


61.50 


7.82 


61.47 


8.09 


61.43 


8.36 


62 


63 


62.53 


7.68 


62.50 


7.95 


62.46 


8.22 


62.42 


8.50 


63 


64 


63.52 


7.80 


63.49 


8.08 


63.45 


8.35 


63.42 


8.63 


64 


65 


64.52 


7.92 


64.48 


8.20 


64.4-1 


8.48 


64.41 


8.77 


65 


66 


65.51 


8.04 


05.47 


8.33 


65.44 


8.61 


65.40 


8.90 


66 


67 


06 50 


8.17 


66.46 


8. 40 


66.43 


8.75 


66.39 


9.04 


67 


6S 


67.49 


8.29 


67.46 


8.58 


67.42 


8.88 


►67.38 


9.17 


68 


69 


63.49 


8.41 


63.45 


8.71 


63.41 


9.01 


63.37 


9.30 


69 


70 
71 


69.43 


8.53 


69.44 


8.83 


69.40 


9.14 


69.36 


9.44 


70 
71 


70.47 


8.65 


70.43 


8.96 


70.39 


9.27 


70.35 


9.57 


72 


71.48 


8.77 


71.42 


9.09 


71.38 


9.40 


71.34 


9.71 


72 


73 


72.46 


8.90 


72.42 


9.21 


V2 33 


9.. 53 


72.33 


9.84 


73 


74 


73.45 


9.02 


73.41 


9.34 


73.37 


9.66 


73.32 


9.98 


74 


75 


74.44 


9.14 


74.40 


9.46 


74.36 


9.79 


74.31 


10.11 


75 


76 


75.43 


9.26 


75.39 


9.59 


75.35 


9.92 


75.31 


10.25 


76 


77 


76.43 


9.33 


176.33 


9.72 


76.34 


10.05 


76.30 


10.38 


77 


78 


77.42 


9.51 


77.33 


9.84 


77.33 


10.18 


1 77.29 


10.52 


78 


79 


78.41 


9.63 


78.37 


9.97 


1 78.32 


10.31 


78.28 


10.65 


79 


80 
81 


79.40 


9.75 


79.36 


10.10 


79.32 


10.44 


79.27 1 10.79 


80 
81 


80.40 


9.87 


80.35 


10.22 


80.31 


10.57 


'80.26! 10.92 


82 


81.39 


9.99 


'81. .34 


10.35 


81.30 


10.70 


81.25 


11.06 


82 


83 


82.33 


10.12 


,82.34 


10.47 


82.29 


10.83 


82.24 


11.19 


83 


84 


83.37 


10.24 


83.33 


10.60 


83.28 


10.96 


183.23 


11.33 


84 


85 


84.37 


10.36 


84.32 


10.73 


84.27 


11.09 


184.22 


11.46 


85 


86 


85.36 


10.48 


85.31 


10.85 


185.26 


11.23 


185.21 


11.60 


86 


87 


86.35 


10.60 


86.30 


10.93 


86.26 


11.30 


86.21 


11.73 


87 


83 


87.34 


10.72 


87.30 


11.11 


187.25 


11.49 


87.20 


11.87 


88 


89 


88.34 


10.85 


88.29 


11.23 


88.24 


11.62 


88.19 


12.00 


89 


90 
91 


89.33 


10 97 


89.28 


11.36 


89.23 


11.75 


89.18 


12.14 


90 
91 


90.32 


11.09, 


90.27 


11.48 


90.22 


11.83 


90.17 


12.27 


92 


91.31 


11.21 


91.26 


11.61 


91.21 


12.01 


91.16 


12.41 


92 


93 


92.31 


11.33 


92.26 


11.74 


92.20 


12.14 


92.15 


12.54 


93 


94 


93.30 


11.46' 


93.25 


11.86 


93.20 


12.27 


93.14 


12.68 


94 


95 


94.29 


11.58 


94.24 


11.99 


94.19 


12.40 


,94.13 


12.81 


95 


96 


95.23 


11.70 


95.23 


12.12 


95.18 


12.53 


95.12 1 12.95 


96 


97 


96.23 


11.82 


96.22 


12.24 


'96.17 


12.66 


1 96.11 1 13.03 


97 


9S 


97.27 


11.94 


97.22 


12.37 


! 97.16 


12.79 


97.10 


13.22 


9S 


93 


93.26 


12.07 


93.21 


12.49 


98.15 


12.92 


'93.10 


13.35 


99 


100 


99.25 


12.19 


99.20 


12.62 


99.14 


13.05 


1 99.09 


13.49 


100 

J 
1 


Dep. 
83 1 


Lat. 

1 


Dep. 


Lat. 


1 
Dep. 


Lat. 


Dep. 


Lat. 


821 


Deg. jl 821 


Deg. 


i 

^ 82V Deg. 



88 



TRAVERSE TATTLE. 



3 


8 Deg. 


8i Deg. 


H D«g. 


H Deg. 


§ 


Lai. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. Dep. 


1 


0.99 


0.14 


0.99 


0.141 


0.99 


0.15 


0.99 0.15 


' 1 


2 


1.98 


0.28 


1.98 


0.29 i 


1.98 


0.30 


1.98 


0.30 


2 


3 


2.97 


0.42 


2.97 


0.43 


2.97 


0.44 


2.97 


0.46 


3 


4 


3.96 


0.56 


3.96 


0.57 


3.90 


0.59 


3.95 


0.61 


4 


5 


4.95 


0.70 


4.95 


0.72 


4.95 


0.74 


4.94 


0.78 


5 


6 


5.94 


0.84 


5.94 


0.86 


5.93 


0.89 


5.93 


0.91 


6 


7 


6.93 


0.97 


6.93 


1.00 


6.92 


1.03 


6.92 


1.06 7 1 


8 I 7.92 


1.11 


7.92 


1.15 


7.91 


1.18 


7.91 


1 22 *? 1 


9 8.91 


1.25 


8.91 


1.29 


8.90 


1..33 


8.90 


1.37 


9 


10 


9.90 


1.39 


9.90 
10.89 


1.43 
1.58 


9.89 


1.48 


9.88 


1.52 


10 
' 11 


Jl 


10.89 


1 . 53 


10.88 


1.63 


10.87 


1.67 


12 


11.88 


1.67 


11.88 


1.72 


11.87 


1.77 


11.86 


1.83 


12 


13 


12.87 


1.81 


12.87 


1.87 


12.86 


1.92 


12.85 


1.98 


13 


14 


13.86 


1.95 


13.86 


2.01 


13.85 


2.07 


13.84 


2.13 


14 


15 


14.85 


2.09 


14.85 


2.15 


14.84 


2.22 


14.83 


2.28 


15 


16 


15.84 


2.23 


15.84 


2.30 


15.82 


2.36 


15.81 


2.43 


16 


17 


16.83 


2.37 


16.83 


2.44 


16.81 


2.51 


16.80 


2.59 


17 


IS 


17.82 


2.51 


17.81 


2.58 


17.80 


2.66 


17.79 


2.74 


18 


19 


18.82 


2.64 


18.80 


2.73 


18.79 


2.81 


18.78 


2.89 


19 


20 
"27 


19.81 


2.78 


19.79 


2.87 


19.78 
20.77 


2.96 


19.77 


3.04 


20 
"21 


20.80 


2.92 


20.78 


3.01 


3.10 


20.76 


3.19 


22 


21.79 


3.06 


21.77 


3.16 


21.76 


3.25 


21.74 


3.35 


22 


23 


22.78 


3.20 


22.76 


3.30 


22 . 75 


3.40 


22 . 73 


3.50 


23 


24 


23.77 


3.34 


23.75 


3.44 


23.74 


3.55 


23.72 


3.65 


24 


25 


24.76 


3.48 


24.74 


3.59 


24.73 


3.70 


24.71 


3.80 


25 


2G 


25.75 


3.62 


25.73 


3.73 


25.71 


3.84 


! 25.70 


3.96 


26 


27 


26.74 


3.76 


26.72 


3.87 


26.70 


3.99 


126.69 


4.11 


27 


2S 


27.73 


3.90 


27.71 


4.02 


27.69 


4.14 


27.67 


4.26 


28 


29 


28.72 


4.04 


28.70 


4.16 


28.68 


4.29 


28.66 


4.41 


29 


30 


29.71 


4.18 


29.69 


4.30 


29.67 


4.43 


129.65 


4.56 


30 


31 


30.70 


4.31 


30.68 


4.45 


30.66 


4.58 


i 30.64 


4.72 


31 


32 


31.69 


4.45 


31.67 


4.59 


31.65 


4,73 


131.63 


4.87 


32 


33 32.68 


4.59 


32.66 


4.74 


32.64 


4.88 


32.62 


5.02 


33 


34 33.67 


4.73 


33.65 


4.88 


33.63 


5.03 


33.60 


5.17 


34 


35 34.66 


4.87 


34.64 


5.02 


34.62 


5.17 


34.59 


5.32 


35 


36 35.65 


5.01 


35.63 


5.17 


35.00 


5.32 


135.58 


5.48 


36 


37 36.64 


5.15 


36.62 


5.31 


36.59 


5.47 


! 36.57 


5.03 


37 


38 37.63 


5.29 


37.61 


5.45 


37.58 


6.62 


37.56 


5.78 


38 


39 138.63 


5.43 


38.60 


5.60 


38.57 


5.76 


38.55 


5.93 


39 


40 130.61 


5.57 
5.71 


39-59 
40. o8 


5.74 


39.56 


5.91 


39.53 


6.08 


40 
41 


41 


40.60 


5.88 


40.55 


6.06 


40.52 


6.24 


42 


41.59 


5.85 


41.57 


6.03 


41.54 


6.21 


41.51 


6.39 


42 


43 


42.. 58 


5.98 


42.56 


6.17 


42.53 


6.36 


42.50 


6.54 43 1 


44 


43.57 


6.12 


43.54 


6.31 


43.52 


6.. 50 


143.49 


6.69 


44 


4 5 


44.56 


6.26 


44.53 


6.46 


44.51 


6.65 


144.48 


6.85 


45 


46 


45.55 


6.40 


45.52 


G.60 


45.49 


6.80 


145.46 


7.00 


46 


47(46.54 


6.54 


46.5 


6.74 


46.48 


6.95 


146.45 


7.15 


47 


48 


47.53 


6.68 


47.50 


6.89 


47.47 


7.09 


47.44 


7.30 


43 


49 


48.52 


6.82 


48.49 


7.03 


48.46 


7.24 


48.43 


7.45 


49 


50 

3 
2 


49.51 


6.96 


49.48 


7.17 


49.45 


7.39 


49.42 


7.61 


50 


Dep. 

82 1 


Lat. 
3eg. 


Dep. 


Lat. 


D>ep. 


Lat. 


Dep. 


Lat. 


.2 


Oil Deg. 


81| 

1 


Deg. 


8U Deg. 



TKAVERSE TABLE 



89 





8Dcg. 

1 


ni Deg. 


8^ Deg. 


8| Deg. 


2 

3 
o 
? 


Lat. 


Dep. 


T,at,. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


50. 50 


T.lo" 


50.47 


7.32 


50.44 


7.54 


50.41 


7.76 


"51 


(32 


51.49 


7.24 


51.46 


7.46 


51.43 


7.69 


51.39 


7.91 


52 


63 


52.48 


7.38 


52.45 


7.61 


52.42 


7.83 


52.38 


8.06 


53 


54 


53.47 


7.52 


53.44 


7.75 


53.41 


7.98 


53.37 


8.21 


54 


55 


54.46 


7.65 


54.43 


7.89 


54.40 


8.13 


54.36 


8.37 


55 


56 


55.46 


7.79 


55.42 


8.04 


55.38 


8.28 


55.35 


8.52 


56 


57 


56.45 


7.93 


56.41 


8.18 


56.37 


8.43 


56.34 


8.67 


57 


58 


57.44 


8.07 


57.40 


8.32 


57.36 


8.57 


57.32 


8.82 


58 


59 


58.43 


8.21 


58.39 


8.47 


58.35 


8.72 


58.31 


8.98 


69 


GO 


59.42 


8.35 


59.38 


8.61 


59.34 


8.87 


59.30 


9.13 


60 


61 


60.41 


8.49 


60.37 


8.75 


60.33 


9.02 


60.29 


9.28 


61 


62 


61.40 


8.63 


61.36 


8.90 


61.32 


9.16 


61.28 


9.43 


62 


63 


62.39 


8.77 


62.35 


9.04 


62.31 


9.31 


62.27 


9.58 


63 


64 


63.38 


8.91 


63.34 


9.18 


63.30 


9.46 


63.26 


9.74 


64 


65 


64.37 


9.05 


64.33 


9.33 


64.29 


9.61 


64.24 


9.89 


65 


60 


65.36 


9.19 


65.32 


9.47 


65.28 


9.76 


65.23 


10.04 


66 


67 


66.35 


9.32 


66.31 


9.61 


66.26 


9.90 


66.22 


10.19 


67 


68 


67.34 


9.46 


67.30 


9.76 


67.25 


10.05 


67.21 


10.34 


68 


69 


68.33 


9.60 


68.29 


9.90 


68.24 


10.20 


68.20 


10.50 


69 


70 
71 


69.32 


9.74 


69.28 


10.04 


69.23 


10.35 


69.19 


10.65 


70 
71 


70.31 


9.88 


70.27 


10.19 


70.22 


10.49 


70.17 


10.80 


72 


71.30 


10.02 


71.25 


10.33 


71.21 


10.64 


71.16 


10.95 


72 


73 


72.29 


10.16 


72.24 


10.47 


72.20 


10.79 


72.15 


11.10 


73 


74 


73.28 


10.30 


73.23 


10.62 


73.19 


10.94 


73.14 


11.26 


74 


75 


74.27 


10.44 


74.22 


10.76 


74.18 


11.09 


74.13 


11.41 


75 


78 


75.26 


10.58 


75.21 


10.91 


75.17 


11.23 


75.12 


11.56 


76 


77 


76.25 


10.72 


76.20 


11.05 


76.15 


11.38 


76.10 


11.71 


77 


78 


77.24 


10.86 


77.19 


11.19 


77.14 


11.53 


77.09 


11.87 


78 


79 


78.23 


10.99 


78.18 


11.34 


78.13 


11.68 


73.08 


12.02 


79 


80 
81 


79.22 


11.13 


79.17 


11.48 


79.12 


11.82 


79.07 


12.17 


80 
81 


80.21 


11.27 


80.16 


11.62 


80.11 


11.97 


80.06 


12.32 


82 


81.20 


11.41 


81.15 


11.77 


81.10 


12.12 


81.05 


12.47 


82 


83 


82.19 


11.55 


82.14 


11.91 


82.09 


12.27 


82.03 


12.63 


83 


84 


83.18 


11.69 


83.13 


12.05 


83.08 


12.42 


83.02 


12.78 


84 


85 


84.17 


11.83 


84.12 


12.20 


84.0^ 


12.56 


84.01 


12.93 


85 


86 


85.16 


11.97 


85.11 


12.34 


85.0ti 


12.71 


85.00 


13.08 


86 


87 


86.15 


12.11 


86.10 


12.48 


86.04 


12.86 


85.99 


13.23 


87 


88 


87.14 


12.25 


87.09 


12.63 


87.03 


13.01 


86.98 


13.39 


88 


89 


88.13 


12.39 


88.08 


12.77 


88.02 


13.16 


87.96 


13.54 


89 


90 
91 


89.12 
90.11 


12.53 


89.07 


12.91 


89.01 


13.30 


88.95 
89,94 


13.69 


90 
91 


12.66 


90.06 


13.06 


90.00 


13.45 


13.84 


92 


91.10 


12.80 


91.05 


13.20 


90.99 


13.50 


190.93 


14.00 


92 


93 


92.09 


12.94 


92.04 


i3.34 


91.98 


13.75 


91.92 


14.15 


93 


94 


93.09 


13.08 


93.03; 13.49 


92.97 


13.89 


92.91 


14.30 


94 


95 


94.08 


13.22 


1 94.02. 13.63 


93.96 


14.04 


93.89 


14.45 


9-5 


96 


95.07 


13.36 


195.01 


13.78 


94.95 


14.19 


94.88 


14.00 


96 


97 


96.06 


13.50 


i 96.00 


1 13.92 


95.93 


14.34 


95.87 


14.76 


97 


98 


97.05 


13.64 


96.99 


■ 14.06 


96.92 


14.49 


96.86 


14.91 


98 


99 


98.04 


13.78 


97.98 


14.21 


97.91 


14.63 


97. S5 


15.00 


99 


100 

c 

i5 


99.03 


13.92 


98.97 
Dup. 


14.35 


93.90 
Dep. 


14.78 


98.84 


15.21 


100 

"i 
B 

"en 

Q 


Dep. 


Lat. 


Lat. 


Lat. 


Dep. 


Lat. 


82 Dog. 


Oil Deg. 


8U Deg. 


8U Deg. 



90 



TRAVERSE TABLE 



5 


9 E 


>eg. 


9i Deg. 


H 


Deg. 


91 


Leg 


1 

r. 


p 


Lat 


Dep. 


1 Lat. 


Dep. 


Lat. 


Dep. 


i - 
i Lat. 


1 Dep. 


1. 0.99 


0.16 


Ik 99" 


0.16 


1 0.99 


0.17 


0.99 


1 0.17 


"l 


2 


1.9S 


1 0.31 


1.97 


0.32 


i 1.97 


0.33 


1.97 


; 0.34 


2 


3 


2.96 


0.47 


2.96 


0.4S 


2.96 


0.50 


2.96 


0.51 


3 


4 


3.95 


1 0.63 


3.95 


0.64 


3.95 


0.66 


3.94 


0.68 


4 


5 


4.94 


1 0.78 


4.93 


0.80 


4.93 


0.83 


4.93 


0.85 


5 


6 


5.93 


; 0.94 


5.92 


0.96 


5.92 


0.99 


5.91 


1.02 


6 


7i. 6.91 


' 1.10 


0.91 


1.13 


6.90 


1.16 


6.90 


1.19 


7 


8; 7. 90 


1.25 


7.90 


1.29 


1 7.89 


1.32 


7.88 


1.35 


8 


9 


8.89 


1.41 


8.88 


1.45 


8.88 


' of 


8.87 


' 52 





11 


9.83 


1.56 


9.87 


1.61 


1 9.86 
i 10.85 


TsT 


S.8G 


1.09 


10 

n 


10.86 


1.72 


1 10.86 


1.77 


10.84 


1.86 


12 


11.85 


1.88 


11.84 


1.93 


11.84 


1.98 


11.83 


2.03 


12 


13 


12.84 


2.03 


12.83 


2.09 


12.82 


2.15 


12.81 


2.20 


13 


1-4 


13.83 


2.19 


13.82 


2.25 


13.81 


2.31 


13.80 


2 37 


14 


15 


14.82 


2.35 


14.80 


2.41 


14.79 


2.48 


14.78 


2.54 


15 


16 


15.80 


2.5C 


15.79 


2.57 


15.78 


2.64 


15.77 


2.71 


16 


17 


16.79 


2.66 


16.78 


2.73 


16.77 


2.81 


16.7f, 


2.88 


17 


18 


17.78 


2.82 


17.77 


2.89 


17.75 


2.97 


17.74 


3.05 


18 


19 


13.77 


2.97 


18.75 


3.05 


18.74 


3.14 


18.73 


3.22 


19 


20 19.75 


3.13 


19.74 


3.21 


19.73 


3.,30j 


19.71 


3.39 


20 
21 


"21 i 20.74 


3.29 


20.73 


3.33 


20.71 


3.47' 


20.70 


3.56 


22 


21.73 


3.44 


21.71 


3.54 


21.70 


3.63 


21.68 


3.73 


22 


23 


22.72 


3.60 


22.70 


3.70 


22.68 


3.80 


22.67 


3.90 


23 


24 


23.70 


3.75, 


23.69 


3.86 


23.67 


3.96; 


23.65 


4.06 


24 


25 


24.69 


3.91 


24.67 


4.02 


24.66 


4.13 


24.64 


4.23 


25 


26 


25.68 


4.07 


25.66 


4.18 


25.64 


4.29 , 


25.62 


4.40 


26 


27 


26.67 


4.22 


26.65 


4.34 


26.63 


4.46 


26.61 


4.. 57 


27 


2S 27.66 


4.38 


27.64 


4.50 1 


27.62 


4.62 i 


27.00 


4.74 


28 


29 i 28.64 


4.54 


23.62 


4.66 


23.60 


4.79 ! 


28.. 58 


4.91 


29 


so' 29.63 
31 1 30.62 


4.69 


29.61 


4.82 


29.59 


4.951 


29.57 
.30.55 


5.03 
5.25 


30 
31 


4.85! 


30.80 


4.98' 


30.57 


5.I2I 


32 131.61 


5.01 


31.53 


5.14 


31.56 


5.28 


3 1.. 54 


5.42 


32 


33 1 32.59 


5.16 


32.57 


5.30 


32 . 55 


5.45 
5.61 


32.52 


5.59 


33 


34 33.53 


6.32 


33.56 


5.47: 


33.53 


33.51 


5.76 


34 


35 


34.57 


5.43 1 


34.54 


5.63: 


.34.52 


5.78! 


34.49 


5.93 


35 


36 


35.56 


5.63 i 


35.. 53 


5.79; 


35.51 


5.94 


35.48 


6.10 


36 


37 


36.54 


5.79 


36.52 


5.95 


36.49 


6.11 


36.47 


6.27 


37 


3S 


37.53 


5.94 


37.51 


6.11 


37.48 


6.27 


37.45 


6.44 


38 


39 


38.52 


6.10 


33.49 


6.27I 


38.47 


6.44 


38.44 


6.60 


39 


40 


39.51 


6.26 i 


39.48 


6.43; 


39.45 


6.60 


39.42 


6.77 


40 


"ir! 40.50 


6.41 j 


40.47 


6.59 ] 


40.44 


6.77 i 


40.41 


6.94 


41 


42 41.48 


6.57 


41.45 


6.75 1 


41.42 


6.92! 


41.39 


7.1 1 


42 


43 ! 42.47 


6.73! 


42.44 


6.91 


42.41 


7.10, 


42.38 


7.28 


43 


44 1 43.46 


6.88 1 


43.43 


7.07 


43.40 


7.26 ! 


43.36 


7.45 


44 


45 j 44.45 


7.O4I 


44.41 


7.23 


44.38 


7.43 


44.35 


7.62 


45 


46 45.43 


7.20: 


45.40 


7.39 


45.37 


7.59 


45.34 


7.79 , 16 1 


47 1 46.42 


7.35 j 


46.39 


7.55 


46.36 


7.76 


46.32 


7.G6! 17 1 


4& 147.41 


7.51 


47.33 


7.72 


47.34 


7.92 


47.31 


8.13 


18 


49' 48.40 


7.67 


43.36 


7.88 


48.33 


8.09 


48.29 


8.30 


49 


50' 


49.38 


7.82 


49.35 


8.04 


49.32 
Dep. 


8.25 


49.28 


8.47 


50 


= 'l 


Dep. 


Lat. 


Dep. 


Lat. 


Lat.' 


Dep. 


Lat. 


5 
3 


a 1 


81] 


i 
Deg. 1 

1 


80| Deg. 1 

1 


801 


Deg. 


m Deg. 


C3 

.5 



TIIAVKKSK TAF5LK 



91 



p 


9 Beg. 


i 9i Deg. r 9^ Deg. 

i 1' 


9.i Deg. 


V.' 

p 

3 
o 
<t 

"51 


1 

51 


LaU Dep. 


Lat. 
' 50^34 


Dep. 
8.20 


,Lat. 


Dep. 


Lat. 


Dep. 


50 37 


7.98 


i 60.30 


8.42 


50.26 


8.64 


52 


51.36 


8.13 


i 51.32 


8.36 


51.29 


8.58 


,51.25 


8.81 


52 


53 


52 . 35 


8.29 


52.31 


8.62 


52.27- 


8.75 


■52.23 


8.98 


53 


54 53.34 


8.4.'-. 


.53.30 


8.68 


53.26 


8.91 


! 53.22 


9.14 


54 


55 54.32 


8.P-0 


54 28 


8.84 


i .54.25 


9.08 


1 64.21 


9.31 


55 


56 55.31 


8.76 


55.27 


9.00 


55.23: 9.24 


^5.19 


9.48 


56 


57 'nfi. 30 8.92 


56.26 9.16 


156.22; 9.41 


56.18! 9.65 


57 


5S 


57.29 9.07 


57.25 9.32 


1 57.20! 9.57 


57.16 


9.82 


58 


59 


.58.27 


9.23 


58.23 9 48 


j 58.19! 9.74 


! 58.15 


9.9f 


59 


60 


59.26 


9.39 


59.22 9 64 


i 59.18: 9.90 


59.13 


10.10 


60 


61 


60.2.5 


9.. 54 


60.21 ' 9.81 


160.16' 10.07 


60.12 


10.33 


61 


63 


61.24 


9.70 


61.19 9.97 


61.15 110.23 


61. iO 


10.50 


62 


63 


62.22 


9.86 


62.18 10.13 


'62.14; 10.40 


62.09 


10. G7 


63 


64 


63.21 


10.01 


63.17 10.29 63.12 1 10.56 


63.08 


10.84 


64 


65 


64.20 1 10.17 


64.15 , 10.45 


64.11 ' 10.73 


64.06 


11.01 


65 


66 


65.19 I 10.32 


65.14 : 10.61 


i 65.09 1 10.89 


65.05 


11.18 


66 


67 


66.18 


10.48 


66.13 ; 10.77 


: 66.08; 11.06 


66.03 


11.35 


67 


68 


67.16 


10.64 


67.12 10.93 


; 67.97 11.22 


67.02 


11.52 


68 


69 


68.15 


10.79 


68.10 1 11.09 


68.05 


11.39 


68.00 


11.69 


69 


70 

71 


69.14 


10.95 


69.09 i 11.25 


69.04 


11.55 


68.99 11. S5 
1 69.97 1 12.02 


_70 
71 


70.13 


11. li 


70.08 


11.41 


■70.03 


11.72 


72 


71.11 


11.26 


71.06 


11.57 


171.01 


11.88 


70.96 


12.19 


72 


73 


72.10 


11.42 


72.05 


11.73 


! 72.00 


12.05 


71.95 


12.36 


73 


74 


73.09 11.58! 


73.04 


11.89 i 72.99 


12.21 


72.93! 12.53 


74 


75 


74. OS 


11.73] 


74.02 


12.06 


[73.97 


12.38 


73.92 j 12.70 


75 


76 


75.06 


11.89 


75.01 


12.22 


174.96 


12.54 


74.90 12.87 


76 


77 


76.05 


12.05! 


76.00 


12.38 


75.94 


12.71 


75.89 13.04 


77 


78 


77.04 


12.20! 


76.99 i 12. .54 


76.93 


12.87 


76.87 ! 13.21 


73 


79 


78.03 


12.36 1 


77.97 12.70 


77.92 


13.04 


77.86 13.38 


79 


80 
"81 


79.02 


12.51; 


78.96 12.86 


178.90 


13.20 


78.84 13.55 


80 
81 


80.00 


12.67i 


79.95 1 13.02 1179.89 


13.37 


79.83 1 13.72 


82 


80.99 


12.83: 


80.93 


13.18 


80.88 


13.53 


80.82 13.89 


82 


83 


81.98 


12.98! 


81.92 


13.34 


81.86 


13.70 


81.80 14.06 


83 


84 


82.97 


13.14' 


82.91 


13.50 


82.85 


13.86 


82.79 14.23 


84 


85 


83.95 


13.30; 


83.8-9 


13.66 


83.83 


14.03 


83.77 14.39 


85 


86 


84.94 


13.45 


84.83 


13.82 


84.82 


14.19 


84.76 14.56 


86 


87 


85.93 


13.61 


85.87 


13.98 


85.81 


14.36 


85.74 


14.73 


87 


88 


86.92 


13.77 i 


86.86 


14.15 


86.79 


14.. 52 


86.73 


14.90 


88 


89 


87.90 


13.92! 


87.84 


14.31 


87.78 


14.69 


87.71 


15.07 


89 


90 
91 


83.89 
89.88 


14.08 i 
14.24 


88.83 
89.82 


14.47 
14.63 


88.77 1 14.85 


88.70! 15.24 


90 
91 


89.75 15.02 


89.69 j 15.41 


92 


90,87 


14.39 


90.80 


14.79 


90.74 


15.18 


90 67 1 15.58 


92 


93 


91.86 


14.55 


91.79 


14.95 


91.72 


15.35 


91.66 1 15.75 


93 


94 


92.84 


14.70 


92.78 


15.11 


92.71 


15.51 


92.64! 15.92 


94 


95 


93.83 


14.86 1 


93.76 ' 15.27 


I 93.70 15.68 


93.63 16.09 


95 


96 94.82 


15.02! 


94.75 15.43 


94.68 


15.84 


94.61 16.26 


96 


97 95.81 15.17! 


95.74 15.59 195.67 


16.01 


95.60 16 43 


97 


9S 


96.79 15.33 1 


96.73 15.75 


96.66 


16.17 


86.58.16.60 


98 


99 


97.78 115.49! 


97.71 15.91 


97.64 1 16.34 


97.57 


16.77 


99 


100 


98.77 115.64: 


98.70 16.07 


98.63 


16.50 


98.56 


16.93 


iOO 


i 

.2 
Q 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat 


Dep. 


Lat. 


c; 

o 

■J. 

Q 


81 Deer. 


80J Deg. 


80^ Deg. 


80i Deg. 



92 



TRAVERSE TABLE 





10 Deg. 


104 Deg. 


m 


Deg. 


10| Deg. 


C 


3 
















1 


Lat. 


Dep. 


r 

1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dtp. 


'1 


0.98 


0.17 


0.98 


0.18 


0.98 


0.18 


0.93 


0.19 


""1 


2, 1.97 


0.35 


1.97 


0.30 


1.97 


0.38 1 


1.96 


0.37 


'Z 


3 2.95 


0.52 


2.95 


0.53, 


2.95 


0.55 1 


2.95 


U 56 


i 


4 1 3.94 


0.69 


3.94 


0.71, 


3.93 


0.73; 


3.93 


0.75 


4 


5 i 4.92 


0.87 


4.92 


0.89; 


4.92 


0.91 i 


4.91 


93 


5 


6' 5.91 


1.04 


6.90 


1.07' 


5.90 


1.09' 


5.89 


J.12 


6 


7 ' 6.89 


1.22 


6.89 


1.25 


6.88 


1.28' 


S.88 


1.31 


7 


8 ' 7.88 


1.39 


7.87 


1.42 1 


7.87 


1.46! 


7.86 


1.49 


6 


9! 8.86 


1.56 


8.86 


1.60 


8.85 


1.64! 


8.84 


1.68 


9 


10 


9.85 


1.74 


9.84 


1.78 1 


9.83 


1.82! 


9.82 
10.81 


1.87 
2.05 


10 
'Il 


'11 


"10 83 


J.91 il 10.82 


1.96 i 


10.82 


2.00! 


12 ; 11 82 


2.08 1 11.81 


2.14 1 


11.80 


2.19 


11.79 


2.24 


12 


13 


12.80 


2.26 1; 12.79 


2.31 ' 


12.78 


2.37 1 


12.77 


2.42 


13 


14 


13.79 


2.43 1, 13.78 


2.49 i 


13.77 


2.55 1 


13.75 


2.61 


14 


15 


14.77 


2.60 


14.76 


2.67! 


14.75 


2.73| 


14.74 


2. SO 


15 


16 


15.76 


2.78 


15.74 


2.85; 


15.73 


2.92 


15.72 


2.98 


16 


17 


16.74 


2.95 


16.73 


3.03; 


16.72 


3.10 


16.70 3.17 


17 


18 


17.73 


3.13 


17.71 


3.20 


17.70 


3.28 


17.08 3.36 


18 


19 


18.71 


3.30 


18.70 


3.38 


18.68 


3.46 I 


18.67 3.54 


19 


20 
21 


19.70 
20.68 


3.47 


19.68 


3.56 
3.74 j 


19.67 
20.65 


3.64j 
3.83'| 


19.65 j 3.73 


20 
21 


3.65 


20.66 


20.63' 


3.92 


22 


21.67 


3.82 il 21.65 


3.91 ' 


21.63 


4.01 


21.61 


4.10 


22 


23 


22.65 


3.99 122.63 


4.09 


22.61 


4.19 


22.60 


4.29 


23 


24 


23.64 


4.17 ,23.62 


4.27 


23.00 


4.37 


23.58 


4.48 


24 


25 


24.62 


4.-34 124.60 


4.45 : 


24.58 


4.56 


24.56 


4.66 


25 


26 


25.61 


4.51 j 25.59 


4.03 ' 


25.56 


4.74 


25.. 54 


4.85 


26 


27 


26.59 


4.69 


i 26.57 


4.80 


26.55 


4.92 


26.53 


5.04 


27 


28 


27.57 


4.86 


127.55 


4.98; 


27.53 


5.10 


27.51 


5.22 


28 


29 


2S.56 


5.04 


28.54 


5.16: 


28.51 


5.28 


28.49 


5.41 


29 


30 
31 


29.54 
30.53 


5.21 


29.52 


5.34, 


29.. 50 


5.47 
5.60 


29.47 


5.60 

5.78 


30 
31 


5.38 


30.51 


5.52 


30.48 


30.46 


32 


31.51 


5.56 


'31.49 


5.09 1 


31.46 


5.83 


: 31.44 


5.97 


32 


33 


32.50 


5.73 


32.47 


5.87 


32.45 


6.01 


i 32.42 


6.16 


33 


34 


33.48 


5.90 


33.46 


6.05! 


33.43 


6.20 


133.40 


6.34 


34 


35 


34.47 


6.0s 


34.44 


6.23 


34.41 


6.38 


134.39 


6.. 53 


35 


36 


35.45 


6.25 


■35.43 


6.41 


35.40 


6.56 


35.37 


6.71 


3S 


37 


36.44 


6.42 


1 36.41 


6.58 


36.38 


6.74 


136.35 


6.90 


37 


38 


37.42 


6.60 


,37.39 


6.76 


37.36 


6.92 


137.33 


7.09 


33 


39 


33.41 


6.77 


38.38 


6.94! 


38.35 


7,11 


^38.32 


7.27 


39 


40 
41 


39.39 


6.95 
7.12 


[39.36 


7.12 


39.33 


7.29 
' 7.47 


i 39.30 


7.46 


40 


40.38 


; 40.35 


7.30 


40.31 


40.28 


7.65 


41 


42 


41.36 


7.29 i41.33 


7.47 


41.30 


7.65 


i41.26 


7.83 


42 


43 


42.35 


7.47 142.31 


7.65 


42.28 


7.84 


1 42.25 


8.02 


43 


44 


43.33 


7.64 143.30 


7.83 


43.26 


8.02 


[43.23 


8.21 


44 


45 


44.32 


7.81 44.28 


8.01 


44.25 


8.20 


44.21 


8.39 


45 


46 


45.30 


7.99 1 45.27 


8.19 


45.23 


8.38 


45.19 


8.58 


46 


4? 46.29 


8.16 j 46.25 


8.36 


46.21 


8.57 


46.18 


8.77 


47 


4S 47.27 


' 8.34 ! 47.23 


8.54 


47.20 


8.75 


47.16 


8.95 


48 


49 48.26 


! 8.51 i 48.22 


8.72 


48.18 


8.93 


48.14 


9.14 


49 


£0 49.24 
1 j Dop. 


i 8.68 


49.20 


8.90 


49.16 


9.11 


49.12 


9.33 


50 

5 


Lat. 

L>eg. 


1 Dep. 

i 

791 


L.t. 
Deg. 


Dep. 


Lat. 


Dep. 


Lat. 


1 ' 

CO 

5 

1 


80 J 


791 


Deg. 


791 Deg. 



TKAVERSE TABLE. 



93 



c 

51 


10 Deg. 


lOi Deg. 


lOi Deg. 1 


103 Deg. 

i 



.51 


Lat. 


Dep. 

8.86 


Lat. 


Dep.j 


Lat. 


Dep. 


Lat. Dep , 
.50.10 i 9.51 


50.23 


50.19 


9.08 ■160.15 


~9T29~| 


52 


51.21 


9.03 


51.17 


9.25 j 51.13 


9.48 


51.09! 9 70 


52 


53 


52.19 


9.20 


52.15 


9.43 


52.11 


9.66 


52.07 


9.89 ' 


53 


54 


53.18 


9.38 


53.14 


9.61 


53.10 


9.84 


53.05 


10.07 j 


51 


55 


54.16 


9.55 


54.12 


9.79 


54.08 


10.02 


54.03 


10.20 


sri 


56 


55.15 


9.72 1155.11 


9.96 1 


55.06 


10.21 


55.02 


10.45 j 


56 


57 


56.13 


9.90 i 56.09 


10.141 


56.05 


10.39 


56.00 


10.63 I 


57 


58 


57.12 


10.07 57.07: 10.32 1 


57.03 


10.57 


56.98 


10.82 


58 


59 


58.10 


10.25 58.06 10.50 


58.01 


10.75 


57.96 


11.00 


59 


60 


59.09 


10.42 59.04 10.68 1 
10.59 60.03 10.85 1 


59.00 


10.93 


58.95 
59.93 


11.19 
11.38 


00 
~61 


61 60.07 


59.98 


11.12 1 


62 


61.06 


10.77 161.01 11.03 


60.96 


11.30 


60.91 


11.56 


62 


63 


62.04 


10. 94161. 99 11.21 
11.11162.93 11.39 


61.95 


11.48 


61.89 


11.75 


63 


64 


63.03 


62.93 


11.66 


62.88 


11.94 


64 


65 


64.01 


11.29 j 63.96 11.57 163.91 1 


11.85! 


63.86 


12.12 


65 


66 


65.00 


11.46 1164.9') 11.74 


64.89 


12.03! 


64.84 


12.31 


66 


67 


65.98 


11.63.; 65.93 11.92 


65.88 


12.21 ! 


65.82 


12.50 


67 


68 


66.97 


11.81 |! 66.91 12.10 1 


66.86 


12.39 


66.81 


12.68 


68 


69 


67.95 


11.98 1 67. 90 12.28 


67.84 


12.57! 


67.79 


12.87 


69 


70 
71 


68.94 
69.92 


12.16; 68.88 12.46! 
12.33 1 69.87 12.63} 


68.83 


12.76; 
12.94i 


68.77 


13.06 


70 
7] 


69.81 


69.75 


13.24 


72 


70.91 


12.50: 70.85 12.81 j 


70.79 


13.12 1 


70.74 


13.43 


72 


73 


71.89 


12.68 71.83 12.99 


71.78 


13.30; 


71.72 


13.62 


73 


74 


72.88 


12.85 72.82 13.17 


72.76 


13.49: 


72.70 


13.80 


74 


75 


73.86 


13.02 j 73.80 ; 13.35 


73.74 


13.67! 


73.68 


13.99 


75 


76 


74.85 


13.20 174.79 13.52 


74.73 


13.85 1 


74.67 


14.18 


76 


77 


75.83 


13.37 75.77 13.70 1 


75.71 


14.03 


75.65 


14.36 


77 


78 


76.82 


13.54 


76.76 13.88 


76.69 


14.21 


76.63 


14.55 


78 


79 


77.80 


13.72 


77.74 14.06 


77.68 


14.40 


77.61 


14.74 


79 


80 
81 


78.78 


13.89 


78.72 1 14.24 


78.66 


14.58 


78.60 


14.92 


80 
81 


79.77 


14.07 


79.71 ' 14.41 


79.64 


14.76 


179.58 


15.11 


82 


80.75 ; 14.241 


80.69 14.59 


80.63 


14.94 


80.50 


15.29 


82 


83 


81.74 


14.41 


81.68 14.77 


81.01 


15.13 


81.54 


15.48 


83 


84 


82.72 


14.59 


82.66; 14.95 


82.59 


15.31 


82.53 


15.67 


84 


85 


83.71 


14.76 


83.64, 15.13 


83.58 


15.49 


83.51 


15.85 


85 


86 


84.69 1 14.93 


84.63 15.30 


84.56 


15.67 


84.49 


16.04 


86 


87 


85.68 15.11 


85.61 1 15.48 


85.54 


15.85 


85.47 


16.23 


87 


88 


86.66 j 15.28 


86.60 ! 15.66 


86.53 


16.04 


8'3.46 


16.41 


88 


89 


87.65' 15.45 


87.58' 15.84 


87.51 


16.22 


87.44 1 16.60 


89 


•90 
91 


88.63; 15.63 


88.56 


! 16.01 
16.19 


88.49 


16.40 


88.42 


16.79 
16.97 


90 
91 


89.62* 15.80 


89.55 


89.48 


16.58 


89.40 


92 


90.60 15.98 


90.53 16.37 


90.46 


16.77 


90.39 1 17.16 


92 


93 


91.59 16.15 


91.52 16.55 


91.44 


16.95 


91.37 1 17.35 


S3 


94 92.57 i 16.32 


92.50 16.73 


92.43 


17.13 


92.35 


1 17.53 


94 


95 93.56 16.50 


93.48! 16.90 


93.41 


17.31 


93.33 


17.72 


95 


96 * 94.54: 16.67 


94.47 ■ 17.08 


94.39 


17.49 


94.32 


17.91 


, 96 


97 95.53 16.84 


95.45 17.26 


95.38 


17.68 


95.30 


18.09 


' 97 


98 96.51; 17.02 


96.44 17.44 


96.36 


17.86 


96.28 


IS. 28 


' 98 


99 


1 97.50 17.19 


97.42 17.62 


97.34 


18.04 


97.26 


1 18.47 


' 99 


100 

u 

i5 


98.48 : 17.36 


98.40 17.79 


98.33 


18.22 


98.25 18.65 


.00 




c 


Dep. 1 Lat. 


Dep. j Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


80 Deg. 


79} Deg. 


791 Deg. 


79i Deg. 

! 



94 



TRAVERSK TABLE. 



1 


11 Deg. 


lU Deg. 


Hi 


J)eg. 


11. f Deg. 


K 

SS 

3 

2 
1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

0.98 


Dep. 
0.20 


I Lat. 1 Dep. 

' 1 


" 0'.9S 


0.19 


0.93 


0.20 


' 0.98! 0.20 


2 


1.96 


0..38 


1.96 


0.39 


1.96 


0.40 


1.96 0.41 


2 


3 


2.94 


0.57 


2.94 


0.59 


2.94 


0.60 i 2.94 i 0.61 


d 


1 


3.93 


0.76 


3.92 


0.73 


3.92 


0.80 . 3.92 : 9.82 


1 


5 


4.91 


0.95 


4.90 


0.98 


4.90 


1.00 


4.90 


1.02 


5 


6 


5.89 


i.u' 


5.88 


1.17 


5.88 


1.20 


5.87 


1.22 


6 


7 


6.87 


1..34, 


0.87 


1.37 


6.86 


1.40 


6.85 


1.43 


7 


8 


7.85 


1.53 


7.85 


1.56 


7.84 


1.59 


7.83 


1.63 


8 


9 


8.83 


1.72 


8.83 


1.76 


8.82 


1.79 


8.81 


1.83 


9 


10 


9.82 


1.91 


9.8] 


1.95 


9.80 


1.99 


9.79 


2.04 


10 


11 


10.80 


2.10 


"10.79' 


2.15 


10.78 


2.19 


10.77 


2.24 


11 


12 11.73 


2.29 


11.77 


2.34 


11.7-6 


2.39 


11.75 


2.44 


12 


13, 12.76 


2.48 


12.75 


2.54 


12.74 


2.59 


12.73 


2.65 


13 


14 j 13.74 


2 67 


13.73 


2.73 


13.72 


2.79 


13.71 


2.85 


14 


15 ; 14.72 


2.80 


14.71 


2.93 


14.70 


2.99 


14.69 


3.06 


15 


16 i 15.71 


3.05 


15.69 


3.12 


15.68 


3.19 


15.66 


3.26 


16 


17 16.69 


3.24 


16.67 


3.32 


16.66 


3.39 


16.64 


3.46 


17 


18 [ 17.67 


3.43 


17.65 


3.51 


17.64 


3.59 


17.62 


3.66 


18 


19 \ 18.65 


3.63 


18.63 


3.71 


18.62 


3.79 


18.60 


3. 87 


19 


20 1 19.63 


3.82 


19.62 


3.90 


19.60 


3.99 


19.58 


4.07 


20 


21 : 20.61 


4.01 


20.60 


4.10 


20.. 58 


4.19 


20.. 56 


~4.23 


21 


22 1 21.60 


4.20 


21.58 


4.29 


21.56 


4.39 21.54 


4.43 


22 


23 1 22.58 


4.39 


22.56 


4.49 


22.54 


4.59: 22.52 


4.63 


23 


24! 23.56 


4.58 


,23.54! 4.63 1 


23.52 


4.78, 23.50 


4.39 


24 


25 


24.54 


4.77 


1 24.52 


4.88 


24.50 


4.98 


24.43 


5.09 


25 


26 


25.52 


4.96 


25.50 


5.07 


25.43 


5.18 


25.46 


5. 3 J 


26 


27 


20.50 


5.15 


26.43 


5.27 


26.46 


5.38 


26.43 


5 . 50 


27 


28 j 27.49 


5.. 34 


27.46 


5.46 


27.44 


5.53 


27.41 


5 . 70 


28 


29 28.47 


5.53 


28.44 


5.66 


23.42 


5.78. 


23.39 


5.91 


29 


30,29.45 


5.72 
5.92 


29.42 
30.40 


5.85 
6.05 


29.40 


5.93' 


29.37 


6.11 


30 


31 


30.43 


30.38 


6.18 


30.35 


-6:ji 


31 


32 


31.41 


6.11 


31.39 


6.24 


31.36 


6.38 


31.33 


6.52 


32 


33 


32.39 


6 30 


32.37 


6.44 


32.34 


6.58 


32.31 


6.72 


33 


34 


33 . 38 


6.49 


33.35 


6.63 


33.32 


6.78 


33.29 


6.92 


34 


35 


34.36 


6.68 


i 34.33 


6.83 


34.30 


6.93:134.27 


7.1:5 


35 


36 


35.34 


6.87 


135.31 


7.02 


35.28 


7.18 


35.25 


7.33 


36 


37 


36.32 


7.06 


136.29 


7.22 


36.26 


7.33 


36.22 


7.53 


37 


38 ! 37.30 


7.25 


137.27 


7.41 


37.24 


7.53 


37.20 


7.74 


3S 


39 i 33.23 


7.4-1: 


38.25 


7.61 


38.22 


7.78 


33.18 


7.94 


39 


40 39.27 


7.63 


39.23 1 7.80 


39.20 


7.97 


39.18 


8.15 


40 


41 40.25 


7.82 


40.21 8.00 


40.18 


8.17 


'40.14 


8.35 


41 


42 41 23 


8.01 


41.19 8.19 


41.16 


8.37 


41.12 


8.55 


42 


43 42.21 


8.20 


1 42.17 8.39 


42.14 


8.57 


42.10 


8.76 


43 


44 143.19 


8.40 


43.15 8.53 


43.12 


8.77 j 43.08 


8.96 


44 


4.^ [44.17 


8.59 


1 44.14 8.78 


44.10 


8.97 


44.06 


9.16 


45 


46 45.15 


8.78 


i 45.12 1 8.97 


45.03 


9.17 


45.04 


9.37 


16 


47 : 46.14 


8.97 J46.10 9.17 


46.06 


9.37 


46.02 


9.57 


47 


48 ; 47.12 


9. 16 ii 47.08 9.36 


47.04 


9 . 57 


46.99 


9.7S 


43 


49 148.10 


9.35 143.06 9.-^0 


4b . 02 


9.77 


47.97 


9. 98 


49 


5^ 


49.08 


1 9.54 


1 49J()^:_9^75jj49.00 


9.97 
Lat. 


48.95 
Dep. 


10.18 
Lat. 


50 



5 




Dep. 

79 

1 


Lat. 
Deg. 


Dep. : Lat. 


1 Dep. 

1 _ .. . 


V'^Desr. ' 8^ 


1 

Deg. 1 781 Deg. 

1 



TRA^KSE TABLE. 



95 



o 
o 


11 Deg. 


IH De?. 


1 IH Deg- 


111 Deg, 


i 
C 
S 

fo* 
3 

? 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 Dep. 


"61 


50.06) 9.73 


50.02 


9.95 


49.98 


10.17 


49.93 


10.39 


~51 


52 


51.04 9.92 


51.00 


10.14 


50.96 


10.37 


50.91 


i 10.59 


52 


53 


52.03 10.11 


51.98 


10.34 


51.94 


10.57 


51.89 


! 10.79 


53 


5i 


.153.01 10.30 


52.96 


10.53 


52.92 


10.77 


52.87 


11.00 


54 


55 


153.99 10.49 


53.94 


10.73 


53.90 


10.97 


53.85 


11.20 


55 


56 


54.97 10.69 


54.92 


10.93 


64.88 


11.16 


54.83 


11.40 


56 


57 


55.95 10.88 


55.90 


11.12 


55.86 


11.36 


55.81 


11.61 


57 


58 


56.93 11.07 


56.89 


11.32 


56.84 


11.56 


56.78 


1 11.81 


58 


59 


57.92 11.26 


57.87 


11.51 


57.82 


11.76 


57.76 


12.01 


59 


60 
61 


58.90 1 11.45 


58.85 


11.71 


53.80 


11.96 


58.74 


12.22 
12.42 


60 
61 


59.88 i 11.64 


169.83 


11.90 


59.78 


12.16 


59.72 


63 


60.86 1 11.83 


60.81 


12.10 


60.76 


12.36 


60.70 ! 12.63 


62 


63 


61.84 1 12.02 


61.79 


12.29 


61.74 


12.56 


1 61.63 


12.33 


63 


64 


62.82 ! 12.21 


62.77 


12.49 


62.72 


12.76 


i 62.66 


13.03 


64 


65 


63.81 


12.40 


63.75 


12.63 


63.70 


12.96 


63.64 


13.24 


65 


66 


64.79 


12.59 


64.73 


12.88 


64.63 


13.16 


64.62 


13.44 


66 


67 


65.77 


12.78 


65.71 


13.07 


65.66 


13.36 


65.60 


13.64 


67 


68 


66.75 


12.98 


66.69 


13.27 


66.63 


13.56 


66.58 


13.85 


68 


69 


67.73 


13.17 


67.67 


13.46 


67.61 


13.76 


67.55 ' 14.05 


69 


70 
71 


68.71 
69.70 


13.36 


68.66 


13,66 


68.59 


13.96 


68.53 ; 14.25 


70 
71 


13.55 


69.64 


13.85 


69.57 


14.16 


69.51 


14.46 


72 


70.68 


13.74 


70.62 


14.05 


70.55 


14.35 


70.49 


14.66 


72 


73 


71.66 


13.93 


71.60 


14.24 


71.53 


'4.55 


71.47 


14.87 


73 


74 


72.64 


14.12 


72.58 


14.44 


72.51 


14.75 


72.45 


15.07 


74 


75 


73.62 ! 14.31 


73.56 


14.63 


73.49 


14.95 


73.43 


15.27 


75 


76 


74.60 14.50 


74.54 


14.83 


74.47 


15.15 


74.41 


15.48 


76 


77 


75.59 1 14.69 


75.52 


15.02! 


75.45 


15.35 


75 39 


15.68 


77 


78 


76.57 14.88 


76.50 


15.22: 


76.43 


15.55 


76.37 


15.83 


78 


79 


77.55 1 15.07 


77.43! 15.411 


77.41 


15.75 


77.34 


16.09 


79 


80 
81 


73.53 
79.51 


15.26 


78.46 15.61 


78.39 


15.95 


78.32 


16.29 


80 
81 


15.46 


79.44 15.80 


79.37 


16.15 


79.30 


16.49 


82 


80.49 


15.65 


80.42 


16.00 


80.35 1 16.35 1 


80.28 


16.70 


82 


83 


81.48 


15.84 


81.41 


16.19 


81.33 1 


16.55 


81.26 


16.90 


83 


84 


82.46 


16.03 


82.39 


16.39 


82.31 


16.75 j 


82.24 


17.11 


84 


85 


83.44 


16.22 


83.37 


16.58 


83.29 


16.95 1 


83.22 


17.31 


85 


86 


84.42 


16.41 


84.35 


16.78 


84.27 


17.15 


84.20 [ 17.51 


86 


87 


85.40 


16.60 


85.33 


16.97 


85.25 


17.35- 


85.18 1 17.72 


87 


83 


86.. 38 


16.79 


86.31 


17.17 


86.23 


17.54 


86.16 17.92 


83 


89 


87.36 


16.98 


87.29 


17.36 


87.21 


17.74 


87.14 18.12 1 


89 


90 
91 


88.35 


17.17 


88.27 


17.56 


88.19 


17.94 


88.11 18.33 1 


90 


89.33 17.36 


89.25 


17.75 1 


89.17 18.14 


89.09 


13.53 


91 


92 


90.31 ! 17.55 


90.23 


17.95 


90.15 18.34 


90.07 


13.74 92 i 


93 i 


91.29 ! 17.75 


91.21 


18.14 


91.13 18.54 


91.05 


18.94 931 


94 


92.27 1 17.94 


92.19 


18.34 


92.11 1 18.74 


92.03 


19.14 


94 


95 


93.25 18.13 


93.17 


13.53 II 


93.09 18.94 


93.01 


19.35 


95 


96 


94.24 18.32 


94.16 


18.73 


94.07 .9.14 


93.99 


19.55 


96 


97 


95.22 18.51 


95.14 


18.92 1 


95.05 19.34 


94.97 


19.75 


97 


98 


96.20 ' 18.70 


96.12 


19.12 1 


96.03 19.54 


95.95 


19.96 


98 


99 


97.18 


18.89 


97.l0i 19.31 


97.01 19.74 


96.93 


20.16 


99 


100 

Q 
1 


98.16 


19.08 


93.081 19.51 


97.99 19.94 


97.90 


20.36 lOOl 


Dep. I 


Lat. 


Dep. 


Lat. 1 


Dep. 1 Lat. 


Dep. 


Lat. 


5 


79 Deg. 


11 
781 Deg. 78| Deg. 


78J Deg. 



96 



TRAVFT?SK TAPLE. 



p 


12Deg 


m Deg. 


m 


De^. 


12| Deg. 


X 


1 


Lat. 


Dep. 
0.21 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
0.98 


Dep. 
0.22 


1 


'0.98 


0.98 


0.21 


0.98 


0.22 


2 


1.96 


0.42 


1.95 


0.42 


1.95 


0.43 


1.95 


0.44 


2 


3 


2.93 


0.62 


2.93 


0.64 


2.93 


0.65 


2.93 


0.66 


3 


4 


3.91 


0.83 


3.91 


0.85 


3.91 


0.87 


3.90 


0.88 


i 


5 


4.89 


1.04 


4.89 


1.06 


4.88 


1.08 


4.88 


1.10 


5 


6 


5.87 


1.25 


5.S6 


1.27 


5.86 


1.30 


5.85 


1.32 S 2 


7 


6.85 


1.46 


6.84 


1.49! 


6.83 


1.52 


6.83 


1 54 


7 


8 


7.83 


1.66 


7.82 


1.70 


7.81 


1.73 


7.80 


1 77 


8 


9i 8.80 


1.87 


8.80 


1.9i: 


8.79 


1.95 


8.78 


1.99 


9 


10 ! 


9.78 


2.08 1 


9.77 


2.12, 


9.76 
10.74 


2.16 


9.75 


2.21 


10 


'll i 


10.76 


2.29 


10.75 


2.33 


2.38 


10.73 


2.43 11 


12 11.74 


2.49 


11.73 


2.55 1 


11.72 


2.60 


11.70 


2.65 \ 12 


13 12.72 


2.70 


12.70 


2.76 


12.69 


2.81 


12.68 


2.87 ^ 13 


14 13.69 


2.91 


13.68 


2.97; 


13.67 


3.03 


13.65 


3.09 14 


15 14.67 


3.12 


14.66 


3.18! 


14.64 


3.25 


14.63 


3.31 ; 15 


16 i 15.65 


3.33 


15.64 


3.39 


15.62 


3.46 


15.61 


3. .53 1 16 


17 16.63 


3.. 53 


16.61 


3.61 


16.60 


3.68 


16.58 


3.75 1 17 


18 17.61 


3.74 


17.59 


3.82 


17.. 57 


3.90 


17. C6 


3.97 ; 13 


19 18.. 58 


3.95 


18.57 


4.03 


18.55 


4.11 


18.53 


4.19 ■ 19 


20 19.. 56 


4.16 


19.54 


4.24 


19.53 


4.33 


19.51 


4.41 ! 20 


21 20.54 


4.371 


20 . 52 


4.46 


20.50 


4.55 1120.48 


4.63 1 21 


22 21.52 


4.57' 


21.50 


4.67 


21.48 


4.76 121.46 


4.86 


22 


23 22.50 


4.78 i 


22.48 


4.88 


22.45 


4.93 ; 22.43 


5.08 


23 


24 23.48 


4.99 1 


23.45 


5.09 


23.43 


5.19 123.41 


5.30 


24 


25 24.45 


5.20 1 24.43 


5.30 


24.41 


5.41 t 24.33 


5.. 52 


25 


2G 25.43 


5.41 11 25.41 


5.52 


25.33 


5.63 25.36 


5.74 


26 


27 26.41 


5.61 


26.39 


5.73 


26.36 


5. 84 26.33 


5.96 


27 


23 27.39 


5.82 


27.36 


5.94 


27.34 


6.06. 27.31 


6.18 23 


29 28.37 


6.03 


28.34 


6.15 


23.31 


6.23 1 28.23 


6.40 ■ 29 


30 129.34 


6.24 1 


29.32 


6.37 


29.29 


6.49 


29.26 
30.24 


6.62 ' 30 
6.84 31 


31 30.32 


6.45' 


30.29 


6.58; 


30.27 


6.71 


32 31.. 30 


6.65 


31.27 


6.79 


31.24 


6.93 31.21 


7.06 , 32 


33 32.28 


6.86 


32.25 


7.00' 


32.22 


7.14 32.19 


7.28 1 33 


34 33.26 


7.07 


33.23 


7.21 


33.19 


7.36 33.16 


7.50 1 34 


35 34.24 


7.28 


34.20 


7.43 


34.17 


7.53 34.14 


7.72 


35 


36 35.21 


7.48 


35.18 


7.64 


35.15 


7.79 35.11 


7.95 


36 


37 36.19 


7.69 


36.16 


7.85 


36.12 


8.01 1 36.09 


8.17 


37 


38 37.17 


7.90 


37.13 


8.06 


37.10 


8.22! 37.06 


8.39 


33 


39 38.15 


8.11 


39.11 


8.27 


33.08 


8.44 33.04 


8.61 


39 


40 139.13 


8.32 


39.09 


8.49 
8.70 


39.05 


8.66 

8.87 


39.01 


8.83 


40 


41 i 40.10 


8.52 


40.07 


40.03 


39.99 


9.05 


41 


42 ; 41.08 


8.73 


141.04 


8.91 


41.00 


9.09 1 40.96 


9.27 


42 


43 42.06 


8.94 


14?. 02 


9.12 


41.98 


9.31 i 41.94 


9.49 


43 


44 43.04 


9.15 


'43.00 


9.34 


42.96 


9.52 j 42.92 


9.71 1 44 


45 44.02 


9.36 


43.93 


9.55 


43.93 


9.74 1 43.89 


9.93 , 45 


46 44.99 


9.56 


44.95 


9.76 


44.91 


9.96 44.87 


10.15 1 46 


47 45.97 


9.77 


45 . 93 


9.97 


' 45.89 


10.17 45.84 


10.371 47 1 


48 


46.95 


9.98 


46.91 


10.18 


48.86 


10.39 46.82 


10.59 


ig 


49 


47.93 


10.19 


47.88 


10.40 


47.84 


10.61 47.79 


10.81 


49 


5C 

i 

i 


48.91 


10.40 


48.86 


10.61 


48.81 


10.82 
Lat. 


43.77 


i 11.03 


50 


Dep. 


Lat. 


Dep. 

771 


Lat. 
Deg. 


Dep. 


; Dep. 


Lat. 


78 


Deg. 


77| 


Deg. 


II m 


Deg. 


5 



TRAVERSE TABLE. 



97 



o 

P 

51 


12 Deg. 


121 Deg. 


12i Deg. 


121 Deg. 


1 C 
1 

"51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


49.89 


TO^GO" 


49.84 


10.82 


49.79 i 11.04 


49.74 


11.26 


52 


50.86 


10.8] 


50.82 


11.03 


50.77 


11.25 


50.72 


11.48 


52 


53 


51.84 


11.02 


.'^1.79 


11.25 


51.74 


11.47 


51.69 1 11.70 


63 


54 


52.82 


11.23 


52.77 


11.46 


52.72 


11.69 


52.67 


11.92 


54 


55 


63.80 


11.44 


.53.75 


! 11.67 


53.70 


11.90 


53.64 


12.14 


55 


56 


54.78 


11.64 


54.72 


' 11.88 


54.67 


12.12 


54.62 


12.36 


5G 


57 


55.75 


11.85 


55.70 


12.09 


55.65 


12.34 


55.59 


12.. 58 


57 


58 


56.73 


12.06 


56.68 


12.31 


56.63 i 12.55 


56.57 


12.80 


58 


59 


57.71 


12.27 


57.66 


12.52 


57.60 


I5i.77 


57.55 


13.02 


59 


60 
61 


58.69 


12.47 


58.63 


12.73 
12.94 


58.58 


12.99 


58.52 


13.24 


60 
'61 


59.67 


12.68 


59.61 


159.55 


13.20 


59.50 


13.46 


62 


60.65 


12.89 


60.59 


13.16 


60.53 


13.42 


60.47 


13.68 


62 


63 


61.62 


13.10 


61.57 


13.37 


61.51 


13.64 


61.45 


13.90 


63 


64 


62.60 


13.31 


62.54 


13.58 


62.48 


13.85 


62.42 


14.12 1 64 


65 


63.58 


13.51 


63.52 


13.79 


63.46 


14.07 


63.40 


14.35) 65 


66 


64.56 


13.72 


64.50 


14.00 


64.44 


14.29 


64.37 


14.57 


66 


67 


65.54 


13.93 


65.47 


14.22 


65.41 


14.50 


65.35 


14.79 


G7 


68 


G6.51 


14.14 


66.45 


14.43 


166.39 


14.72 


66.32 


15.01 


68 


69 


67.49 


14.35 


67.43 


14.64 


; 67.36 


14.93 


67.30 


15.23 


ogr 


70 
71 


68.47 


14.55 


68.41 


14.85 


! 68.34 


15.15 


68.27 


15.45 


70 
71 


69.45 


14.76 


69.. 38 


15.06 


169.32 


15.37 


69.25 


15.67 


72 


70.43 


14.97 


70.36 


15.28 


70.29 


15.58 


70.22 


15.89 


72 


73 


71.40 


15.18 


71.34 


15.49 


171.27 


15.80 


71.20 


16.11 


73 


74 


72.38 


15.39 


72.32 


15.70 


! 72.25 


16.02 


72.18 


16.33 


74 


75 


73.36 


15.59 


73.29 


15.91 


173.22 


16.23 


73.15 


16.55 


75 


76 


74.34 


15.80 


74.27 


16.13 


174.20 


16.45 


74.13 


16.77 


76 


77 


75.32 


16.01 


75.25 


16.34 


!75.17 


16.67 


75.10 


16.99 


77 


78 


76.30 


16.22 


76.22 


16.55 


76.15 


16.88 


76.08 


17.21 


78 


79 


77.27 


16.43 


77,20 


16.76 


77.13 


17.10 


77.05 


17.44 


79 


80 
81 


78.25 


16.63 


78.18 
79.16 


16.97 


78.10 


17.32 


78.03 


17.66 


80 


79.23 


16.84 


17.19 


79.08 


17.53 


79.00 


17.88 


81 


82 


80.21 


17.05 


80.13 


17.40 


80.06 


17.75 


79.98 


18.10 


82 


83 


81.19 


17.26 


81.11 


17.61 


81.03 


17.96 


80.95 


18.32 


83 


84 


82.16 


17.46 


82.09 


17.82 


82.01 


18.18 


81.93 


18.54 


84 


85 


83.14 


17.67 


83.06 


18.04 


82.99 


18.40 


82.90 


18.76 


85 


86 


84.12 


17.88 


84.04 


18.25 


83.96 


18.61 


83.88 


18.98 


86 


87 


85.10 


18.09 


85.02 


18.46 


84.94 


18.83 


84.83 


19.20 


87 


88 


86.08 


18.30 


86.00 


18.67 


85.91 


19.05 


85.83 


19.42 


88 


89 


87.06 


18.50 


86.97 


18.88 


86.89 


IS. 26 


86.81 


19.64 


89 


90 
91 


88.03 


18.71 


87.95 
88.93 


19.10 


87.87 


19.48 


87.78 


19.86 


90 


89.01 


18.92 


19.31 


88. 8i 


19.70 


88.76 


20.08 


91 


92 


89.99 


19.13 


89.91 


19.52 


89.82 


19.91 


89.72 


20.30 


92 


93 


90.97 


19.34 


90.88 


19.73 


90.80 


20.13 


90.71 


20.52 


93 


94 


91.95 


19.54 


91.86 


19.94 


91.77 20.35 


91.68 


20.75 


94 


95 


92.92 


19.75 


92.84 20.16! 


92.75 20.56 


92.66 


20.97 1 95 


96 


93.90 i 19.96 1 


93.81 


20.37 


93.72 20.78 


93.63 


21.19 j 96 


97 


94.88 '20.17 


94.79 


20.58 


94.70 20.99 


94.61 


21.41 ! 97 


98 


95.86 20.38 


95.77 


20.79 


95.68 21.21 


95.58 


21.63 1 99 


99 


96.84:20.58 


96.75 


21.01 


96.65 21.43 


96.66 


21.85 99 


100 


97.91 120.79 


97.72 


21.22 


97.63 21.64 


97.53 


22.07 
Lat. 


100 

i 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


78 Deg. 1 


77J Deg 


77^ Deg. 


TTi Deg. 



98 



TRAVKKSE TABLE. 



I 


13 Deg. 


134 Deg. 


m 


Deg. 


I3.f Deg. 


n 
o 


Lat. 1 Dep. 

1 1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.97 


0.23 


0.97 


0.23 


0.97 


0.23 


0.97 


0.2i 


2 


1.95 


0.45 


1.95 


0.46 


1.95 


0.47 


1.94 


0.48 


2 


3 


2 92 


0.67 


2.92 


0.69 


2.92 


.0.70 


2.91 


0.71 


3 


4 


3.90 


0.90 


3.89 


0.92 


3.89 


0.93 


3.89 


0.95 


4 


.fi 


4.87 


1.12' 


4.87 


1.15 


4.86 


1.17 


4.86 


1.19 


5 


6 


5,85 


1.35 


5.84 


1.38 


5.83 


1.40 


5.83 


1.43 


6 


7 


6.82 


1.57 


0.81 


1.60 


6.81 


1.63 


6. 80 


1.66 


7 


8 


7.80 


1.80 


7.79 


1.83 


7.78 


1.87 


7.77 


1.90 


8 


<J 


8.77 


2.02 


8.76 


2.06 


8.75 


2.10 


8.74 


2.14 


9 


10 
11 


9.74 


2.25 


9.73 


2.29 


9.72 
10.70 


2.33 
2.57 


9.71 


2.38 


10 


10.72 


2.47 


10.71 


2.52 


10.68 


2.61 


11 


12 


11.69 


2.70; 


11.68 


2.75 


11.67 


2.80 


11.66 


2.85 


12 


13 


12.67 


2.92 


12.65 


2.98 


12.64 


3.03 


12.63 


3.09 


13 


14 


13.64 


3.151 


13.63 


3.21 


13.61 


3.27 


13.60 


3.33 


14 


15 


14.6;J 


3.37 


14.60 


3.44 


14.59 


3.. 50 


14.57 


3.57 


15 


16 


15.59 


3.60! 


15.57 


3.67 


15.56 


3.74 


15.54 


3.8C 


16 


17 


16.57 


3.82 1 


10.55 


3.90 


16.53 


3.97 


16.51 


4.04 


17 


18 


17.54 


4.05! 


17.52 


4.13 


17.50 


4.20 


17.48 


4.28 


18 


19 


18.51 


4.27 


18.49 


4.35 


18.48 


4.44 


18.46 


4.52 


19 


20 


19.49 


4.50 


19.47 


4. 58 


19.45 


4.67 


19.43 


4.75 


20 


21 


20.46 


4.72 


20.44 


4.81 


20.42 


4.90 


20.40 


4.99 


21 


22 


21.44 


4.95 


21.41 


5.04 


21.39 


5.14 


21.37 


5.23 
5.47 


22 


23 


22.41 


5.17 


22.39 


5.27 


22.. 36 


5.37 


22.34 


23 


24 


23.38 


5.40 


23.36 


5.50 


23 . 34 


5.60 


23.31 


5.70 


24 


25 


24.36 


5.62 


24.33 


5.73 


24.31 


5.84 


24.28 


5.94 


25 


26 


25.33 


5.85 


25.31 


5.96 


25 . 28 


6.07 


25.25 


6.18 


26 


27 


26.31 


6.07 


26.28 


6.19 


26.25 


6.30 


26.23 


6.42 


27 


28 


27.28 


6.30 


27.25 


6.42 


27.23 


6.. 54 


27.20 


6.60 


28 


29 


28.26 


6.52 


28.23 


6.65 


28.20 


6.77 


28.17 


6.89 


29 


30 
31 


29.23 
30.21 


6.75 
6.97 


29.20 
30.17 


6.88 
7.11 


29.17 


7.00 


29.14 
30.11 


7.13 
7.37 


30 
31 


30.14 


7.24 


32 


31.18 


7.20 


31.15 


7.33 


31.12 


7.47 


31.08 


7.61 


32 


33 


32.15 


7.42 


32.12 


7.56 


32.09 


7.70 


32.05 


7.84 


33 


34 


33.13 


7.65 


33.09 


7.79 


33.06 


7.94 


33.03 


8.08 


34 


35 


34.10 


7.87 


34.07 


8.02 


34.03 


8.17 


34.00 


8.32 


35 


36 


35.08 


8.10 


35.04 


8.25 


35.01 


8.40 


34.97 


8.56 


36 


37 


36.05 


8.32" 


36.02 


8.48 


35.98 


8.64 


35.94 


8.79 


37 


38 


37.03 


8.55 


36.99 


8.71 


36.95 


8.87 


.36.91 


9.03 


38 


39 


38.00 


8.77 


37.96 


8.94 


37.92 


9.10 


37.88 


9.27 


39 


40 


38.97 


9.00 


38.94 


9.17 


38.89 


9.34 


38.85 


9.51 


40 


41' 


39.95 


9.22 


39.91 


9.40 


39.87 


9.57 


39.83 


9.75 


41 


42 


40.92 


9.45 


40.88 


9.63 


40.84 


9.80 


40.80 


9.98 


42 


43 


41.90 


9 67 


41.86 


9.86 


41.81 


10.04 


41.77 


10.22 


43 


44 


42.87 


9.90 


42.83 


19.08 


42. 7S 


1 10.27 


42.74 


10.46 


44 


45 


43.85 


i0.12 


43.80 


10.31 


43.76 


1 10.51 


43.71 


10.70 


45 


46 ' 44.82 


10.35 


44.78 


10.54 


44.73 


' 10.74 


44.68 


10.93 


46 


i7 


45.80 


10.57 


45.75 


10.77 


45.70 


10.97 


45.65 


11.17 


47 


48 


46 77 


10.80 


46.72 


11.00 


46.67 


11.21 


46.62 


11.41 


! 48 


49 


47.74 


11.02 


47.70 


11.23 


47.65 


11.44 


47.60 


11.65 


49 


50 


48.72 


11.25 


48.67 


11.46 


48.62 


11.67 


48.57 


11.88 


£0 


o 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lut. 


1 

Q 


77 Deg. 


761 Deg. 


76J 


Deg. 


76^ 


Deg. 



TRAVERSE TABLE. 



99 



1 

"51 


13Deg 


13i Deg. 


131 Deg. 


131 Deg. 


1 


p 

5l 


Lat. 


Dep. 


Lat. 1 Dep. 


Lat. 
'A9759 


Dep. 

11.91 


Lat. 


Dep. 


49.69 


11.47 


49.64 1 11.69 


49.54 


12.12 


52 


50.67 


11.70 50.62 11.92 


50.. 56 


12.1411 50.51 
12.37 51.48 


12.36 


52 


53 


51.64 


11.92 51.59 12.15 


51.54 


12.60 


53 


54 


52.62 


12.15 1 52.56 12.38 


52.51 


12.61 52.45 


12.84 


54 


55 


53.59' 12.37 !| 53.54 1 12.61 


53.48 


12.84; 53.42 


13.07 


55 


66 1 54.56, 12.60 Ij 54.51 12.84 


54.45 


13.07 54.40 


13.31 


56 


57 155.54; 12.82:155.48 13.06 


55.43 


13.31 55.37 


13.55 


57 


58 


50.51 1 13.05 


56.46 13.29 


.56.40 


13.. 54 156.34 


13.79 


58 


59 


57.49 1 13.27 


57.43 1 13.52 


57.37 


13.77 11 57.31 


14.02 


59 


60 


58.46 1 13.50 


53.40 


13.75 


58.34 


14.01 j: 58.28 


14.26 


60 


'61 


59.44 


13.72 


59.38 


13.98 


59.31 


14.24 1: .59.25 1 14.50 


61 


62 


60.41 


13.95 


60.35 


14.21 


60.29 


14.47 1 


60.22 


14.74 


62 


63 


61.39 


14.17 


61.32 


14.44 


61.26 


14.71 


61.19 


14.97 


63 


64 


62.36 


14.40 


62.30 


14.67 


62.23 


14.94: 


62.17 


15.21 


64 


65 


63.33 


14.62 


63.27 


14.90 


63.20 


15.17, 


63.14 


15.45 


65 


66 


64.31 


14.85 


G4.24 115.13 


64.18 


15.41 ! 


61.11 


15.69 


66 


67 


65. 2S 


15.07 


65.22! 15.36 


65.15 


15.64, 


65.08 


15.93 


67 


68 


66.26 


15.30 


66.19 


15.59 


66.12 


15.871 


66.05 


16.16 


68 


69 


87.23 


15.52 


67. IC 


15.81 


67.09i 16.11 i 


67.02 


16.40 


69 


70 

71 


68.21 
69.18 


15.75 
15.97 


68.14 


16.04 


68.07 


16.34 


67.99 


16.64 
16.88' 


70 

"71 


69.11 


16.27 


69.04 


16.57 II 68.97 


72 


70.15 


16.20 


70.08 


16.50 


70.01 


16.81;! 69.94 


17.11 


72 


73 


71.13 


16.42 


71.06 


16.73 


70.98 


17.04 1 


70.91 


17.35 


73 


74 


72.10 


16.65 


72.03 


16.96 


71.96' 17.28 


71.88 


17.59 


74 


75 


73.08 


16.87 


173.00 


17.19 


72.93 j 17.50 


72.85 


17.83 


75 


76 


74.05 


17.10 


73.93 


17.42 


73.90 17.74: 


73.82 


18.06 


76 


77 


75.03 


17.32 


74.95 


17.65 


74.87 17.98 


74.79 


18.30 


77 


78 


76.00 


17.55 


75.92 


17.88 


75.84! 18.21 


75.76 


18.54 


78 


79 


76.98 


17.77 


76.90 18.11 i 


76.82; 18.44: 


76.74 


18.78 


79 


80 
81 


77.95 
78.92" 


18.00 


77.87 


18.34 
18.57 


77.79 1 18.68 , 


77.71 


19.01 


80 
81 


18.22 


78.84 


73.76' 18.91 ! 


78.68 


19.25 


82 


79.90 


18.45 


79.82 


18.79 


79.73 


19.14! 


79.65 


19.49 


82 


83 ,80.87 


18.67 


80.79 


19.02 


80.71 


19.38 i 


80.62 


19.73 


83 


84 81.85 


18.90 


81.76 


19.25 


81.68 


19.61 \ 


81.59 


19.97 


84 


85 1 82.82 


19.12 


82.74 


19.48 


82.65! 19.84! 


82.56 


20.20 


85 


86 i 83.80 


19.35 


83.71 


19.71 


83.62 ■ 20.08 183.54 


20.44 


86 


87 184.77 


19.57 


84.68 


19.94 


84.60 20.31 |! 84.51 


20.68 


87 


88 185.74 


19.80 


85.66 


20.17 


85.57 20.54 il 85.48 


20.92 


88 


89! 86.72 


20.02 


86.63 


20.40 


86.54 20.78 | 86.45 


21.15 


89 


90 87.69 


20.25 


87.60 


20.63 


87.51 i 21.01 1 87.42 


21.39 


90 


91 88.67 


20.47 


88.58 


20.86 


88.49 21.24 88.39 121.63, 91 | 


92 89.64 


20.70 


89.55 i 21.09 


89.46 21.48 189.36 


21.87 


92 


93 90.62 


20.92 


90.52 2^ 32 


90.43 21.71 


90.33 


22.10 


93 


94 91.59 


21.15 


91.50 21.54 


91.40 21.94 


91.31 


22.34 


94 


95 92.57 


21.37 


92.47 21.77 


92.33 22.18 


92.28 


22.58 


95 


96, 93.54 


21.60 


93.44 22.00 


93.35 22.41 


93.25 


22.82 


96 


97 


94.51 


21.82 


94.42 22.23 


94.32 22.64 


94.22 


23.06 


97 


93 


95.49 


22,05 


95.39 22.46 


95.29 22.88 


95.19 


23.29 , 9S| 


99 


96.46; 22.27 


96.36 22.69 


96.26 23.11 


96.16 


23.53 


99 


100 


97.44 


22.50 
Lat. 

Deg. 


97.34 , 22.92 


97.24 23.34 


97.13 


23 77 


100 

8 

5 


1 

.2 


Dop. 

77 


Bcp. 1 Lat. ; 


Dep. 1 Lat. 


Dep. 


Lat. 


76! Deg. ' 76^ l)cg. 


76J Deg. 



21 



100 



TRAVERSE TALLE. 



5 

3S 
P , 

3 ! 

n ' 
a 


14 DQg. 


14iDeg. : 

1 


14i 


Deg. 

i 


141 ] 


[)eg. 

1 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 


Lat. 


Dep. i 


"i 


0.97! 


0.24 


0.97 


0.25 1 


0.97 


0.25; 


0.97 


0.25 


"1 


2 


1.94 


0.48 


1.94 


0.49 


1.94 


0.50 


1.93 


0.51 


2 


3 


2.91 


0.73 


2.91 


0.74 


2.90 


0.75 


2.90 


0.76 


3 


4 


3.88 1 


0.97 


3.83 


0.98 1 


3.87 


1.00 


3.87 


1.02 


4 


5 


4.85! 


1.21 


4. 85 


1.23! 


4.84 


1.25 


4.84 


1.27 


c 


6 


5.82 


1.45 


5.82 


1.4SI 


5.81 


I..50: 


5.80 


1.53 1 


G 


7 6.79; 


1.69 1 6. 78 
1.94 7.75 


1 72! 


6.78 


1.75 1 


6.77 


1.73; 




8. 7.76! 


1.971 


7.75 


2.00 


7.74 


2.04 i 


3 


9 


8.73! 


2.13 1 S.72 2.22 1 


8.71 


2.25 1 


8.70 


2.29 


9 


10 


9.701 


2.42; 9.69 1 2.46 1 


9.63 


2.50 


9.67 


2.55 


10 


iJ 


10.67 


2.66 li 10.66 


2.71 1 


10.65 


2.75! 


10.64 


2.80 


U 


13 


11.04 i 


2.90 1 11.63 


2.95' 


11.62 


3.00; 


11.60 


3.06 


12 


13 


12.61 


3.15 


12.60 


3.20 1 


12.59 


3.25! 


12.57 


3.31 


13 


14 


13.53 


3.39 


13.57 


3.45' 


13.55 


3.51! 


13.54 


3.56 


14 


15 


14.55 1 


3.63 


14.54 


3.69 ; 


14.52 


3.76' 


14.51 


3.32 


15 


16 


15.52; 


3.87 


15.51 


3.94! 


15.40 


4.01 


15.47 


4.07 


16 


17 


16.50 1 


4.11 


16.43 


4.18 


16.48 


4.26 


16.44 


4.33 


17 


18 


17.47 1 


4.35 


17.45 


4.43; 


17.43 


4.51 


17.41 


4.58 


18 


19 


18.441 


4.60 


18.42 


4.63 


13.39 


4.76 


18.37 


4. 84 


19 


20 
21 


19.41 I 


4.84 


19.33 


4.92 


19.36 


5.01 


19.34 
20.31 


5.09 


20 
21 


20.33; 


5.03 


20.35 


5.17 


20.33 


5.26 


5.35 


22 


21.35: 


5.32 


21.32 


5.42 


21.30 


5.51 


21.28 


5.60 


22 


23 


22.32 


5.56 


22.29 


5.66 


22.27 


5.76 


22.24 


5.86 


23 


24 


23.99 


5.31 


,23.26 


5.91 


23.24 


6.01 


23.21 


6.11 


24 


25 


24.26 


6.05 


124.23 


6.15 


24.20 


6.26 


24.13 


6.37 


25 


26 


25.23 


6.29 


i 25.20 


6.40 


25.17 


6.51 


25.14 


6.62 


26 


27 


26.20 


6.53 


j 26.17 


6.65 


26.14 


6.76 


20.11 


6.87 


27 


28 


27.17 


6.77 


27.14 


6.89 


27.11 


7.01 


127.08 


7.13 


23 


29 


23.14' 


7.02 


28.11 


7.14 


28.08 


7.20 


123.04 


7.33 


29 


30 
31 


29.11 
30.08 


7.26 
7.50 


29.08 


7.38 


29.04 


7.51 


i 29.01 


7.64 

7.89 


30 
31 


30.05 


7.63 


30.01 


1 7.76 


129.93 


32 


31.05 


7.74 


31.02 


7.83 


30,93 


8.01 


130.95 


8.15 


32 


33 


32.02 


7.93 


131.93 


8.12 


31.95 


8.26 1131.91 


8.40 


33 


34 


32.99 


8.23 


32.95 


8.. ^7 


.32.92 


8.51 


; 32.83 


8.60 


34 


35 


33.95 


8.47 


1 33.92 


8.62 


33.89 


8.78 


! 33.85 


8.91 


35 


36 


34.93 


8.71 


i 34.89 


8.8S 


34.85 


9.01 


34.81 


9.17 


38 


37 


35.90 


8.95 


135.86 


9.11 


35.82 


i 9.28 


35.73 


9.42 


37 


38 


36.87 


9.19 


136.83 


9.35 


! 3G.79 


! 9.51;! 36. 75 


9.67 


33 


39 


37.84 


9.44 


! 37.80 


9.60 


37.76 


i 9.78 11.37.71 


9.93 


39 


40 
41 


33.81 
39.78 


9.63 
9.92 


133.77 


9.85 


33.73 
39.69 


1 10.02 
1 10.27 


1 33.68 


10.13 


40 

41 


39.74 


10.09 


39.65 


1 10.44 


42 


40.75 


10.16 


40.71 


10.34 


40.63 


10.52 


40.62 


10.69 


42 


43 


41.72 


10.40 


i41.03 10.53 


41.63 


10.77 


141.58 


10.95 


43 


44 


42.69 


10.64 


142.65 10.83 


142.60 


j 11.02 


142.55 


11.20 


44 


45 


43.66 


10.89 


43.62 11.08 


i 43.57 


11.27 


143.52 


11.46 


45 


40 


44.63 


11.13 


I44.5S i 11.32 !| 44.53 


1 11.52 


44.48 


11.71 


46 


47 45.60 


11.37 


45.55 11.57 


45.50 


I 11.77 


,45.45 


: 11.97 


1 ** ' 


• 43 46.57 


11.61 


46.. 52 11.82 


46.47 


12.02 


46.42 


1 12.22 


! 43 


49 '47.54 


11.85 


147.49 12.06 


47.44 


12.27 


47.39 


1 12 43 


49 


60 

c 
cd 


143.51 


12.10 


148.46! 12.31 


43.41 


12.52 


1 48.35 


i 12 73 


50 

V 

w 


JDep. 


Lat. 


1 Dep. 

i — 


1 Lat. 


Dep. 


1 Lat. !! Dep. 


1 Lat. 


5 


76] 


Deg. 


75 1 Deg. 


1 751 

1 


Deg. 


j 75i 

1 


Deg. 


Ir. 



TRAVERSE TABLE. 



101 



f» 

s 
n 
o 


14 Deg. 


14i Deg. 


ui 


Deg. 


14| Deg. 


rr.' 

£"• 

ffl . 

"51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

12.98 


49.49 


12.34 


49.43 


12.65 


49.38 


12.77 


49.32 


52 


50.46 


12.58 


50.40 


12.80 


50.34 


13.02 


50.29 


13.24 


52 


53 


51.43 


12.82 


51.37 


13.05 


51.31 


13.27 


51.25 


13.49 


53 


54 


52.40 


13.06 


52.34 


13.29 


52.28 


13.52 


52.22 


13.75 


54 


55 


53.37 


13.31 


53.31 


13.54 


63.25 


13.77 


53.19 


14.00 


55 


56 


54.34 


13.55 


54.28 


13.78 


54.22 


14.02 


54.15 


14.26 


5(5 


5-^ 


55.31 


13.79 


55.25 


14.03 


55.18 


14.27 


.55.12 


14.61 


57 


58 


56.28 


14.03 


56.22 


14.28 


56.15 


14.52 


56.09 


14.77 


58 


59 


57.25 


14.27 


57.18 


14.52 


57.12 


14.77 


57.06 


15.02 


59 


60 
61 


58.22 


14.52 


68.15 


14.77 


58.09 


15.02 


58.02 


15.28 


60 
61 


59.19 


14.76 


59.12 


16.02 


59.06 


15.27 


58.99 


15.53 


62 


60.16 


15.00 


60.09 


15.26 


60.03 


15.62 


59.96 


15.79 


62 


63 


61.13 


15.24 


61.06 


15.51 


60.99 


15.77 


60.92 


16.04 


63 


64 


62.10 


15.48 


62.03 


15.75 


61.96 


16.02 


61.69 


16.29 


64 


65 


63.07 


15.72 


63.00 


16.00 


62.93 


16.27 


62.86 


16.55 


65 


66 


04.04 


15.97 


63.97 


16.25 


63.90 


16.53 


63.83 


16.80 


66 


67 


65.01 


16.21 


64.94 


16.49 


64.87 


16.78 


64.79 


17.06 


67 


68 


65.98 


16.45 


65.91 


16.74 


65.83 


17.03 


65 . 76 


17.31 


68 


69 


66.95 


16.69 


66.88 


16.98 


66.80 


17.28 


66.73 


17.57 


69 


70 

71 


67.92 


16.93 
17.18 


67.85 


17.23 


67.77 


17.53 


67.69 


17.82 
18.08 


71 


68.89 


68.82 


17.48 


68.74 


17.78 


68.66 


72 


69.86 


17.42 


69.78 


17.72 


69.71 


18.03 


69.63 


18.33 


72 


73 


70.83 


17.66 


70.75 


17.97 


70.67 


18.28 


70.59 


18.59 


73 


74 


71.80 


17.90 


71.72 


18.22 


71.64 


18.53 


71.56 


18.84 


74 


75 


72 77 


18.14 


72.69 


18.46 


72.61 


18.78 


72.53 


19.10 


75 


76 


73.74 


18.39 


73.66 


18.71 


73.58 


19.03 


73.60 


19.35 


76 


77 


74.71 


18.63 


74.63 


18.95 


74.55 


19.28 


74.46 


19.60 


77 


78 


75.68 


18.87 


75.60 


19.20 


75.52 


19.53 


75.43 


19.86 


78 


79 


76.65 


19.11 


76.57 


19.45 


76.48 


19.78 


76.40 


20.11 


79 


80 
81 


77.62 
78.59 


19.35 


77.54 


19.69 


77.45 


20.03 


77.36 


20.37 


80 


19.60 


78.51 


19.94 


78.42 


20.28 


78.33 


20.62 


81 


82 


79.56 


19.84 


79.48 


20.18 


79.39 


20.53 


79.30 


20.88 


82 


83 


80.53 


20.08 


80.45 


20.43 


80.36 


20.78 


80.26 


21.13 


83 


84 


81.50 


20.32 


81.42 


20.68 


81.32 


21.03 


81.23 


21.39 


84 


85 


82.48 


20.56 


82.38 


20.92 


82.29 


21.28 


82.20 


21.64 


85 


86 


83.45 


20.81 


83.35 21.171 


83.26 


21.53 


83.17 


21.90 


86 


87 


84.42 


21.05 


84.32 


21.42 


84.23 


21.78 


84.13 


22.15 


87 


88 


85.39 


21.29 


85.29 


21.66 


85.20 


22.03 


85.10 22.41 


88 


89 


86.36 


21.53 


86.26 


21.91 


86.17 


22.28 


86.07 


22.66 


89 


90 
91 


87.33 


21.77 


87.23 


22.15 


87.13 


22.. 53 


87.03 


22.91 
23.17 


90 
91 
92 


88.30 1 22.01 


88.20 


22.40 


88.10 


22.78 


88.00 


92 


89.27 


22.26 


89.17 


22.65 


89.07 


23.04 


88.97 


23.42 


93 


90.24 


22.50 


90.14 


22.89 


90.04 


23.29 


89.94 


23.68 


93 


94 


91.21 


22.74 


91.11 


23.14 


91.01 


23.. 54 


90.90 


23.93 


94 


95 


92.18 


22.98 


92.08 


23.38 


91.97 


23.79 


91.87 


24.19 


95 


96 


93.15 


23.22 


93.05 123.63 


92.94 


24.04 


92.84 


24.44 


96 


97 


94.12 


23.47 


94.02 123.88 


93.91 


24.29 


93.80 


24.70 


97 


93 


95.09 


23.71 


94.98 


24.12 


94.88 


24.54 


94.77 


24.95 


98 


99 


96.06 i 23 95 


95.95 


24.37 


95.85 


24.79 


95.74 


25.21 


99 
100 


100 

ei 
P 


97.03 


24.19 


96.92 


24.62 


96.81 


25.04 
Lat. 


96.70 


25.46 


Dep. 


Lat. 


Dep. 1 Lat. 

' 1 


Dep. 


Dep. 


Lat. 


s 


76 Deg. 


75| Deg 


75 i Deg. 


75i Deg 



102 



TRAVERSE TABLE. 



1 

f 


15 Deg. 


I 
15i Deg. j 

i 


15^ 


Deg. 


151 


Dag. 


1 
§ 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


l! 0.97 


0.26 1 


0.96 


0.26 


0.99 


0.27 


0.96 


0.27 


2: 1.93 


0.52 


1.93 


0.53 


1.93 


0.53 


1.92 


0.54 


2 


3 1 2.90 


0.78 


2.89 


0.79 


Ji.S9 


0.80 


2.89 


0.81 


3 


4 , 3.86 


1.04 


3.86 


1.05 


3.85 


1.07 


3.85 


1.09 


4 


5 1.83 


1.29 


4.82 


1.32 


4.82 


1.34 


4.81 


1.36 


5 


6 6.80 


1.55 


5.79 


1.53 


5.78 


1.60 i 


5.77 


1.63 


6 


7 1 r..76 


1.81 


6.75 


1.84 


6.75 


1.87 


6.74 


1.90 


7 


8 


7.73 


2.07 


7.72 


2.10 


7.71 


2.14 


7.70 


2.17 


8 


9 


8.69 


2.33 


8.68 


2.37 ! 


8.67 


2.41 


8.66 


2.44 


9 


10 

11 


9.66 


2.59 


9.65 


2.63 I 


9.64 


2.67 


9.62 


2.71 


lU 


10.63 


2.85 


10.61 


2.89 


10.60 


2.94! 


10.59 


2.99 


11 


12 


11.59 


3.11 


11. .58 


3.16 


11.56 


3.21 1 


11.55 


3.26 


12 


13 


12.56 


3.38 


12.. 54 


3.42 i 


12.53 


3.47 1 


12.51 


3.53 


13 


U 


13.52 


3.62 


13.51 


3.63 


13.49 


3.74; 


13.47 


3.80 


14 


15 


14.49 


3.83 


14.47 


3.95 


14.45 


4.01 i 


14.44 


4.07 


15 


16 


15.45 


4.14 


15.44 


4.21 


15.42 


4.23 1 


15.40 


4.34 


16 


17 


16.42 


4.40 


16.40 


4.47 
4.73 


16.33 


4.54 1 


16.36 


4.61 


17 


IS 


17.39 


4.66 


17.37 


17.35 


4.81 


17.32 


4.89 


18 


19 


18.35 


4.92 


18.33 


5.00 , 


13.31 


5.03 |! 13.29 


5.16 


19 


20 
21 


19.32 
20.28 


5.18 
5.44 


19.30 


5.26 


19.27 


5.34:' 19.25 


5.43 


20 
21 


20.26 


5.. 52 


20.24 


5.61 20.21 


5.70 


22 


21.25 


5.69 


21.23 


5.79 


21.20 


5.83 21.17 


5.97 


22 


23 


22.22 


5.95 


22.19 


6.05 


22.16 


6.15 22.14 


6.24 


23 


24 


23.18 


6.21 


23.15 


6.31 1 


23.13 


6.41 ,23.10 


6.51 


24 


25 


24.15 


6.47 


24.12 


6. .53: 


24.09 


6.63 


24.06 


6.79 


25 


26 


25.11 


6.73 


25.08 


6.84 i 


25.05 


6.95 


25.02 


7.0b 


26 


27 


26.03 


6.99 


26.05 


7.IO1 


26.02 


7.22 


25.99 


7.33 


27 


28 


27.05 


7.25 


27.01 


7.36 


26.93 


7.43 


26.95 


7.60 


23 


29 


23.01 


7.51 


27.93 


7.63 


27.95 


7.75 


27.91 


7.87 


29 


30 
31 


23.93 


7.76 


1 28.94 
29.91 


7.89: 
8.15 


23.91 


8.02 


2S.87 


8.14 
8.41 


30 
31 


29.94 


8.02 


29.87 


8.23 


29.84 


32 


30.91 


8.28 


30.87 


8.42 


30.84 


8.55 


30.80 


8.69 


32 


33 


01.83 


8.54 


131.84 


8.68 


31.80 


8.82 


31.70 


8.96 


33 


34 


32.84 


8.80 


32.80 


8.94 


32.76 


9.09 


32.72 


9.23 


34 


35 


33.81 


9.06 


33.77 


9.21 


33.73 


9.35 


33.69 


9.50 


35 


36 


34.77 


9.32 


34.73 


9.47 


34.69 


9.62 


34.65 


9.77 


36 


37 


35.74 


9.58 


35.70 


9.73 


35.65 


9.89 


35.61 


10.04 


37 


38 


.36.71 


9.84 


36.66 


10.00 


36.62 


10.16 


36.. 57 


10.31 


33 


39 


37.67 


10.09 


37.63 


10.26 


37.53 


10.42 


37.. 54 


10.59 


39 


40 


33.64 


10.35 


33.59 
139.56 


10.52 


33.55 


10.69 
10.96 


j 38.50 
j 39.40 


; 10.^1 

; 11.13 


10 
41 


41 


39.60 


10.61 


10.73 


39.51 


42 40.57 


10.87 


! 40 . 52 


11.05 


40.47 


11.22 


: 40,42 


1 11.40 


42 


43 


41.53 


11.13 


1 41.49 


11.31 


41.44 


11.49 ;j41.39 


i 11.67 


43 


44 


42.50 


11.39 


1 42.45 


11.57 


142.40 


11.76 ii 42.35 


; 11.94 


44 


45 


43.47 


11.65 


: 43.42 


11.84 


,43.36 


12.03 :43.31 


i 12.21 


45 


46 


44.43 


': 11.91 


44.33 


12.10 


144.33 


1 12.29 1:44.27 


1 12.49 


40 


47 45.40 


12.16 


45.35 


12.36 


,45.29 


1 12.56 1; 45. 24 


1 12.76 


47 


48 46.36 


, 12.42 


46.31 


12.63 


46.25 


1 12.83 1146.20 


13.03 


43 


49 47.33 


12.63 47.27 


12.89 


1 47.22 


1 13.09 U7.1(> 


13.30 


49 


50 (48.30 


12.94 48.24 


13.15 


■43.18 


1 13.36 


||48.12 


13.57 


50 

6 

c 


"1 

1 


j Dep. 


1 Lat. ij Dep. 


Lat 


Dep. 


Lat. 


! Dep. 


1 Lat. 


75 


Deg. 1 74i 


Deg. 


741 


Deg. 74.i 


Deg. 


s 

i 



TRAVEKSE TABLE. 



103 



P. 

P 

3 
o 
a 

"51 


15 Dcg. 


15| Deg 

1 


15^ Deg. 


15J Deg. 


1 
51 


Lat. 


Dep. 
13.20 


Lat. 


Dep. 


Lat. Dep. 
49.15; 13.63' 


Lat. Dep. 


49.26 


49.29 


13.41 


49.09 13.84 


52 


50.23 13.46 


50.17 


13.68 


50.11 


13.90, 


.50.05 U.ll 


52 


53 


51.19 1 13.72 


51.13! 13.941 


51.07 


14.16! 


51.01 U,39 


53 


64 


52.16 1 13.98 


52.10 ' 14.20 


52.04 


14.43 


51 97 14. 6G 


54 


65 


53. IS 14.24 


53.06 ! 14.47 


53.00 


14.70 


52.94 14.93 


5£ 


56 


54. U9 , 14.49 ii 54.03 14.73 


53.96 


14.97 


.53.90! 15.20 


56 


67 


55.06 i 14.75 1 


,54.99 1 14.99, 


54.93 


15.23 1 54.86 \ 15.47 


57 


68 


56.02 i 15.01 


55.96 1 15.26 1 


55 . 89 


15. .50 1 55.82 i 15.74 


58 


59 


56.99 115.27 


56.92 15.52 \ 


56.85 


15.77 


56.78 . 16.01 


59 


60 


57.96 ' 15.53 


57.89 i 15.78 | 


57.82 


16.03 1 


57.75 1 16.29 


60 


61 


58.92 ; 15.79 1 


58.85 1 16.04! 


58.78 1 18.30 1 


58.71 i 16.56 


61 


62 


59.89 


16.05 


59.82 j 16.31 i 


59.75 


16.57 1 


59.67 


16.83 


62 


63 


60.85 


16.31 


60.78 i 16.57 1 


60.71 


16.841 


60.63 


17.10 


63 


64 


61.82 


16.56 


61.75 


16.83; 


61.67 


17.10! 


01.60 


17.37 


64 


65! 


62.79 


16.82 


62.71 


17.101 


62.64 


17.371 


62.56 


17.64 


65 


66 , 


63.75 


17.08 


63.68 


17.35 1 


63.60 


17.64 


63.52 


17.92 


66 


67 1 


64.72 


17.34 


64.04 


17.62 1 


64.56 


17.90 


64.48 


18.19 


67 


68 : 


65.68 


17.60 


65.61 


17.89 : 


65.53 


18.17 


65.45 


18.46 


68 


69 


66.65 


17.86 


66.571 18.15; 


66.49 


18.4-11 


66.41 


18.73 


69 


70 1 

"^1 


67.61 


18.12 


67.54: 18.41 1 
68.-50 i 18.68 i 


67.45 


18.711 


67.37 


19.00 


70 
71 


68.58 


18.38 


68.42 i 18.97! 


68.33 


19.27 


72 ! 


69.55 


18.63 


69.46 ' 18.94! 


69.38 ' 19.24; 


69.30 19.54 


72 


73 


70.51 


18.89 1 


70.43 , 19.20, 


70.35' 19.51 1 


70.26 19.82 


73 


74 


71.48 


19.151 


71.39 19.46 1 


71.31 


19.78; 


71.22 20.09 


74 


75 


72.44 


19.41 


72.36 


19.73 1 


72.27 


20.041 


72.18 120.86 


75 


76 


73.41 


19.67 


73.32 


19.99, 


73.24 


20.31 1 


73.15 1 20.63 


76 


77 


74.38 


19.93 


74.29 


20.25' 


74.20 


20.58' 


74.11 20.90 


77 


78 


75.34 


20.19 1 


75.25 


20.52 ; 


75.16 


20.84 1 


75.07 


21.17 


78 


79 


76.31 


20.45 


76.22 1 20.78 1 


76.13 121.11 1 


76.03 


21.44 


79 


80 
81 


77.27 


20.71 


77.18 : 21.04 
78.15 '21.31 i 


77.09 


21.38 1 


77.00 


21.72 


80 
"SI 


78.24 


20.96 


78.05 


21.65 


77.96 


21.99 


82 


79.21 


21.22 


79.11 


21.57 


79.02 


21.91 ! 78.92 


22.26 


82 


83 


80.17 


21.48 


80.08 


21.83 


79.98 


22.18 ! 79.88 


22.53 


83 


84 


81.14 


21.74 


81.04 


22.09 


80.94 


22.45 ,80.85 


22.80 


8'1- 


85 


82.10 


22.00 


'82.01 


22.36 


81.91 


22.72 181.81 


23.07 


85 


86 


83.07 


22.26 


82.97 


22.62 


82.87 


22.98 1 82.77 


23.34 


86 


87 


84.04 


22.52 


; 83.94 122.88 


83.84 


23.25 


83.73 


23.62 


87 


88 


85.00 


22.78. 


84.90 23.15 


84.89 


23.. 52 


84.70 


23.89 


88 


89 


85.97 


23.03 


■85.87 23.41 


85.76 


23.78 


85.66 


24.16 


89 


90 
91 


86.93 


23.29 


186.83 23.67 


1 86.73 


24.05 


' 86.62 


24.43 


90 
91 


87.90 ! 23.55 


87.80 123.94 


'87.69 


24.32 


87.58 


24.70 


92 


88.87 123.81 


88.76 24.20 


'88.65 


24.59 


: 88.55 


24.97 


92 


93 


89.83 124.07 


89.73 1 24.46 


189.62 


24.85 


i 89.51 


25.24 


93 


94 


90.80 24.33 


90.69 ; 24.72 


190.58 '25.12 


190.47 


25.52 


94 


95 


91.76 24.59 


91.65 124.99 


1 91 54 25.39 


: 91.43 ; 25.79 


9.^ 


96 


92 73 124.85 


92.62' 25.25 


192.51 ,25.65 


92.40 120.06 


96 


97 


93.69 25.11 


93.58 125.51 


93.47 25.92 ' 93.36 26.33 


97 


98 


94.66 25.36 


194.55 125.78 


94.44i26.l9l9t. 32 26.60 


9S 


99 


95.03 25.62 


■95.51 126.04 


95.40 i 26.46 ' 95.28 26.87 


90 


100 

§ 

.2 


96.59 25.88 


36.4.S 


'26.30 


96.36 126.72 : 96>25 | 27.14 


100 

i ~ 


Dep. Lat. 


Dep. 


Lat. 


Dep. Lat. | Dep. 


Lat. 


75 Deg. 1; 741 Ueg. 


74^ Deg. U\ Deg. 



104 



TRAVERSE iABLE. 



II 

C : 16 Deg. \\ iQk Deg. 


16^ 


Deg. 


16| Deg. 





1 

a 
1 


Lat. ' 


! 












\ 


m 


Dep. ! 

1 


Lat. 


Dep. 


Lat. 


Dep. 

~0 23"! 


Lat. 


Dep. ! 


0.96 


0.28' 


0.96 


0.28 


0.96 


0.96 


0.29 


2 


1 92 


55 i 1.92 


0.56 


1.92 


0.57 


1.92 


0.58 


2 


3 


2.S8 


C 83 'i 2.88 


0.84 


2. 83 


0.85 


2.87 


0.86 


3 


4 


3.85 


1.10: 3.84 


1.12 1 


3.84 


i.u; 


3.83 


1.15- i 


5 


4.81 


1.33 i 4.80 


1.40 


4.79 


1.42! 


4.79 


1.44 1 5 


6 


5.77 


1.65: 


5.76 


1.63 


5.75 


1.70. 


5.75 


1.73 1 6 


7 


6.73 


1.93i 


0.72 


1.96 1 


6.71 


1.99 1 


0.70 


2.03 7 


8 


7.69 


2.21 : 


7.68 


2.24 ! 


7.67 


2.27 1 


7.66 


2.31 8 


9 


8.65 


2.48: 


8.64 


2.52 i 


8.63 


2.56 1 


8.62 


2.59 9 


10 
11 


9.01 


2.76 


9.60 


2.80 1 


9.59 


2.84! 


9.58 


2.83 


10 


10. .57 


3.03 ! 10.56 


3.08 : 


10.55 


3.12 


10.53 


3.17 1 


IT 


1 o 


11.54 


3.31 'i 11.52 


3.36 : 


11.51 


3.41 


11.49 


3.46 


12 


13 


12.50 


3.. 58:1 12.48 


3.64 i 


12.46 


3.69 


12.45 


3.75 


13 


14 


13.46 


3.86 i 13.44 


3.92 ll 13.42 


3.98 


13.41 


4.03 


14 


15 


14.42 


4.13 1 14.40 


4.20 1 


14.33 


4.26: 


14.36 


4.32 


15 


16 


15.38 


4.41 !| 15.36 


-4.48 


15.34 


4.54 i 15.32 


4.61 


16 


17 


16.34 


4.69 i 


16.32 


4.76 


16.30 


4.83 ;i 16.28 


4.90 


17 


18 


17.30 


4.961 


17.28 


5.04 


17.26 


5.11 ! 17.24 


5.19 


18 


19 


18.23 


5.24: 


18.24 


5.32 


18.22 


5.40 1 18.19 


5.48 


19 


20 


19.23 


5.51! 


19.20 


5.60 


19.18 


5.08 :' 19.15 


5.76 
6.05 


20 

21 


21 


20.19 


5.79 1 


20.16 


5.88 


20.14 


5.96 1 


20.11 


23 


21.15 


6.06 1| 21.12 


6.16 


21.09 


6.25 


21.07 


6.34 


22 


23 


22.11 


6.34!, 22.08 


6.44 


122.05 


6.53 


22.02 


6.63 


23 


21 


23.07 


6.62; 


23.04 


6.72 


123.01 


6.82, 


23.98 


6.92 


24 


25 


24.03 


6.89 


24.00 


7.00 


23.97 


7.10 


23.94 


7.20 


25 


26 


24.99 


7.17 


24.96 


7.28 


; 24.93 


7.38 


24.90 


7.49 


26 


27 


25 . 95 


7.44 


25.92 


7.56 


125.89 


7.67. 


25.85 


7.78 


27 


28 


26.92 


7.72 


26.88 


7.84 


26.85 


7.95 1 


26.81 


8.07 


23 


29 


27.83 


7.99 


27.84 


8.11 


27.81 


8.24 


27.77 


8.36 


29 


30 
31 


23.84 


8.27 


23.80 


8.39 


28.76 


8.53 I 


28.73 


8.65 


30 


29.80 


8.54 


29.76 


8.67 


29.72 


8.80 


29.63 


8.93 


31 


32 


30.76 


8.83i 


30.72 


8.95 


30.63 


9.09 


30.64 


9.22 


32 


33 


31.73 


9.io; 


31.68 


9.23 


31.64 


9.37 


31.60 


9.51 


33 


34 


33.68 


9.37 


33.64 


9.51 


33.60 


9.06 


32.56 


9.80 


34 


35 


.33.64 


9.65: 


33.60 


9.79 


33.56 


9.94 


33.51 


10.09 


35 


36 


34.61 


9.92 1 


34.56 


10.07 


34.53 


10.22 


31.47 


10.38 


36 


37 


35.57 


10.20 1 


35 53 


10.35 


35.43 


10.51 


35.43 


10.66 


37 


38 


36.53 


10.47 


35.48 


10.63 


36.44 


10.79 


36.. 39 


10.95 


33 


39 


37.49 


10.75 


37.44 


10.91 


37.39 


11.08 


37.35 


11.24 


39 


40 
41 


38.45 
39.41 


11.03 


38.40 


11.19 


38.35 


11.36 


38.30 


11.53 


40 
41 


11.30 


39.36 


11.47 


39.31 


11.64 


39.30 


11.82 


42 


40.37 


11.58 


40.33 


11.75 


40.27 


11.93 


40.23 


12.10 


42 


43 


41.33 


11.85 


41.23 


12.03 


41.23 


13.21 


41.18 


12.39 


1 43 


41 


42.30 


13.13 


13 . 24 


12.31 


42.19 


12.50 


43.13 


13.68 ; 44 1 


45 


43.23 


13.40 


43.20 


12.59 


43.15 


12.78 


43.00 


13.07 45 1 


46 


44.22 


12.63 


44.16 


12.87 


44.11 


13.08 


44.05 


13.23 


1 46 


47 


45.18 


12.95 


45.12 


13.15 


45. OG 


13.35 


45.01 


13.55 


47 


48 


46.14 


13.23 


46.03 


13.43 


148.02 


13.63 


45.96 


13.83 


1 48 


49 


47.10 


13.51 


47.04 


13.71 


146.93 


13.93 


46.92 


14.12 


1 49 


50 


48.03 


13.78 


43.00 


13.99 


47.91: 


14.20 


47.83 


14.41 


1 50 


6 


Dep. 


j Lat. 


Dep. 

i 731 


Lat. 
Deg. 


Dep. 


Lat. 


Dep. 


Lat. 


i i 

'1 


74 


Deg. 


■^ 


Deg. 


734 Deg. 



TKA.VERSE TABLE. 



105 



^1 

p 

3 
o 
o 

5l i 


16 Deg. 


m Oeg. 


16A Deg 

i 


161 Deg. 


K 

3 
o 

CD 

51 


Lat. ! Dep. j 
49.02 14.06 


Lat. 


Dep. 
14.27 


Lat. Dep. 


Lat. 


Dep. 


48.96 


48.90 14.48 48.84 1 


14.70 


52 1 


49.99 14.33 


49.92 


14.55 


49 86; 14.77 


49.79 


14.99 


52 


53. 


.50.95 14.61 


50.88 


14 83! 50.82 i 15.05] 


50.75 


15.27 


53 


54 


51.91 1 14.88 1 


51.84 


15 11 !! 51.78 1 15.34! 


51.71 


15.56 


54 


55 1 


52.87 ' 15.16 1 


52.80 


15.39 !i 52.74 1 15.62 1 


52.67 


15.85 


55 


56 


.53.83 15.44 


53.76 


15.67 


53.69 15.90 1 


53.62 


16.14 


56 


57 


.54.79 '15.71 1 


54.72 


15.95 


54.65 16.19 


54.53 


16.43 


57 


53 


55.75 15,99 1 


55.68 


16.23 


55.61 16.471 


55.54 


16.72 


58 


59 


56.71 


16.26 


56.64 


16.51 


56.57 1 


16.76! 


56.50 


17.00 


59 


60 1 
"61 ' 


57.68 


16.54| 


57.60 
.58.56 


16.79 1 


57.53} 
58.49 


17.04] 
17.32 i 


57.45 


17.29 


60 
'61 


.58.64 


16.81 1 


17.07 


58.41 1 


17.58 


62 


59.60 


17.09 


59.52 


17.35 


59.45 


17.61; 59.37 


17.87 


62 


63 


60.56 


17.37 


50 48 


17.63 


60.41 


17.89' 60.33 


18.16 


63 


64 


61.52 1 


17.64 


61.44 


17.91 


61.36 


18.18i 61.28 


18.44 


64 


65 ; 62.48 1 


17.92 i 


62.40 


18.19 


62.32 


18.46 1 62.24 


18.73 


65 


66 163.44 


18.19 1 


63.33 


18.47 


63.28 


18.74 ; 63.20 


19.02 


60 


67 164.40 


18.47! 


64.32 


18.75 


64.24 


19.03 164.16 


19.31 


67 


68 


65.37 


18.741 


65.28 


19.03 


65.20 


19.31 ; 65.11 


19.60 


68 


69 


66.33 


19.02^ 


66.24 


19.31 


66.16 


19.60 


66.07 


19.89 


69 


70 
71 


67.29 ! 19.29 , 


67.20 
68.16 


19.59 
19.87 


67.12 
68.08 


19.88 


67.03 


20.17 


70 
71 


68.25 19.57, 


20.17 1 


67.99 


20.46 


72 


69.21 19.85 


69.12 


20.15 


69.03 


20.45 i 


68.95 


20.75 


72 


73 


70.17 


20.12 


70.08 


20.43 


69.99 


20.73 


69.90 


21.04 


73 


74 


71.13 


20.40 


71.04 


20.71 


70.95 


21.02 


70.86 


21.33 


74 


75 


72.09 


20.67 


72.00 


20.99 


71.91 


21.30 


71.82 


21.61 


75 


76 


73.06 


20.95; 


72.96 


21.27 


72.87 


21.59 


72.78 


21.90 


76 


77 


74.02 


21.221 


73.92 


21.55 


73.83 


21.87 


73.73 


22.19 


77 


78 


74.98 


21.50 1 


74.88 


21.83 


74.79 


22.15 


74.69 


22.48 


78 


79 


75.94 


21.78 


75.84 


22.11 


75.75 


22.44 


75.65 


22.77 


79 


80 
"81 


76.90 
77.86 


22.05 


76.80 
77.76 


22.39 


76.71 


22.72 


76.61 


23.06 
23.34 


RO 
81 


22.33 


22.67 


77.66 


23.01 


77.56 


82 


78.82 


22.60 


78.72 


22.95 


78.62 


23.29 


78.52 


23.63 


82 


83 


79.78 


22.88 


79.68 


23.23 


79.58 


23.57 


79.48 


23.92 


S3 


84 


80,75 


23.15 


80.64 


23.51 


80.54 


23.86 


80.44 


24.21 


84 


85 


81.71 


23.43 


81.60 


23.79 


81.50 


24.14 


81.39 


24.50 


85 


86 


82.67 


23.70 


82.56 


24.07 


82.46 


24.43 


82.35 


24.78 


66 


87 


83.63 


23.98 


83.52 


24.35 


83.42 


24.71 


83.31 


25.07 


87 


88 


84.59 


24.26 


84.48 


24.62 


84.38 


24.99 


84.27 


25.36 


88 


89 


85.55 


24.53 


85.44 


24.90 


85.33 


25.28 


85.22 


25.65 


89 


90 
91 


80.51 


24.81 


86.40 


25.18 


86.29 


25.56 


86.18 
87.14 


25.94 
26.23 


90 
91 


87.47 


25.08 


87.36 


25.46 


87.25 1 25.85 


92 


,88.44 


25.36 


88.32 


25.74 


88.21 


26.13 


^88.10 


26.51 


92 


93 


189.40 


25.63 


89.28 


26.02 


89.17 


26.41 


89.05 


26.80 


y3 


94 


!90.£6 


25.91 


90.24 


26.30 


90.13 


26.70 


: 90.01 


27.09 


9i 


95 


91.32 


26.19 


91.20 i 26.58 


91.09 


26.98 


90.97 


27 .38 


95 


96 


02.28 


26.46 


92.16 


26.86 ; 92.05^27.27 


91.93 


27.67 


9G 


97 


93.24 


26.741 93.12 


27.14! 93.01 27.55 


02.88 


27.95 


i^'i 


98 


194.20 


27.011 94.08 


27.42 1 93.96 27.83 


93.84 


28.24 


[lis 


99 


195.16 


127.29 95.04 


27.70; 94.92 28.12 


,94.80 


28.53 


99 


100 

Q 


196.13 
Dep. 


27.56' 96.00 [27.98 


95.88 128.40 


195.76 


28.82 


' 3 00 

a 

! ° 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. 


Dep. 


Lat. 


74] 


Deg. 


73f 


Deg. 


73i 


Deg. 


ij '^M Deg. 



106 



TRAVERSE TABLE. 





17 


Deg. 


17i Deg. 


ni 


Dog. 


17| Deg. 


o 


o 

,•1 


J. at. 


Dep. j 


Lat. 


Dep. 


Lat. 
0T95 


Dep. 

0.30 


Lat. 


Dep. 


1 


0.95 


0.29 1 


0.95 


0.30 


0.95 


0.30 


2' 1.91 


0..58 


1.91 


0.59 


1.91 


0.60 


1.90 


0.61 


2 


3 2.87 


0.88 


2.87 


0.89 


2.86 


0.90 1 


2.86 


0.91 


3 


4 3.83 


1.17 


3.82 


1.19 


3.81 


1.20 


3.81 


1 22 


4 


5; 1.78 


1.46 


4.78 


1.48 


4.77 


1..50 


4.76 


1 . .52 


5 


6 5.74 


1.75 


5.73 


1.78 


5.72 


1.80 


5.71 


1.83 


6 


7 6.69 


2.05 


6.69 


2.08 


6.68 


2.10 


6.67 


2 13 


7 


8 7.65 


2.. 34 


7.64 


2.37 


7.63 


2.41 


7.62 


2.44 


8 


9 8.61 


2.63 


8.60 


2.67 


8.58 


2.71 


8 57 


2.74 


9 


10 


9.56 


2.92 


9.55 


2.97 


9.54 


3.01 


9.52 


3.05 


10 
11 


"ii 


10.52 


3 . 22 


10.51 


3.26 


10.49 


3.31 


10.48 


3.35 


12 


11.48 


3.51 


11.46 


3.56 


11.44 


3.61 


11.43 


3.66 


12 


13 


12.43 


3.80 


12.42 


3.85 


12.40 


3.91 


12.. 38 


3.96 


13 


14 


13.39 


4.09 


13.37 


4.15 


13.35 


4.21 


13.33 


4.27 


14 


15 


14.34 


4.39 


14.33 


4.45 


14.31 


4.51 


14.29 


4.57 


15 


16 


15.30 


4.68 


15.28 


4.74 


15.26 


4.81 


15.24 


4.88 


16 


17 


16.26 


4.97 


16.24 


5.04 


16.21 


5.11 


16.19 


5.18 


17 


18 


17.21 


5.26 


17.19 


5.34 


17.17 


5.41 


17.14 


5.40 


18 


19 


18.17 


5.56 


18.15 


6 63 1 


18.12 


5.71 


18.10 


5.79 


19 


20 
21 


19.13 


5.85 


19.10 
20.06 


.5.93 
6.23! 


19.07 
20.03 


6.01 
6.31 


19.05 


6.10 


20 
21 


20.08 


6.14 


20.00 


6.40 


22 


21.04 


6.43 


21.01 


6 52 


20.98 


6.62 


20.95 


6.71 


22 


23 


21.99 


6.72 


21.97 


6.82 


21.94 


6.92 


21.91 


7.01 


23 


24 


22.95 


7.02 


2^.92 


7.12 


22.89 


7.22 


22.86 


7.32 


24 


U 


23.91 


7.31 


23.88 


7 41 


23.84 


7.52 


23.81 


7.62 


25 


24.86 


7.60 


24.83 


7.71 


24.80 


7.82 


24.76 


7.93 


26 


27 


25.82 


7.89 


25.79 


8.01 


25.75 


8.12 


25.71 


8.23 


27 


28 


XC^.7S 


8,19 


26.74 


8.30 


'46.70 


8.42 


26.67 


8.. 54 


28 


29 


27.73 


8.48 


27.70 


8.60 


27.66 


8.72 


27.62 


8.84 


29 


30 
3f 


28 . 69 
29.65 


S.77 
9.06 


28.65 
29.61 


8.90 


28.61 


9.02 


28.57 


9.15 


30 
31 


9.19 


29.57 


9.32 


29.52 


9.45 


32 


30.60 


9.36 


30.56 


9.49 


30.52 


9.62 


30.48 


9.76 


32 


33 


31.56 


9.65 


31. .52 


9.79 


31.47 


9.92 


31.43 


10.06 


33 


34 


82.51 


9.94 


32.47 


10.08 


32.43 


10.22 


32. C8 


10.37 


34 


35 


33.47 


10.23 


33.43 


10.38 


33.38 


10.52 


33.33 


10.67 


35 


36 


34.43 


10.53 


34.. 38 


10.68 


34.33 


10.83 


34.29 


10.98 


36 


37 


35.38 


10.82 


.35.34 


10.97 


35.29 


11.13 


35 24 


11.28 


37 


38 


36.34 


11.11 


36.29 


11.27 


36.24 


11.43 


36.19 


11.58 


38 


39 


37.30 


11.40 


37.25 


11.57 


37.19 


11.73 


37.14 


11.89 


39 


40 

41 


38.25 


11.09 


38.20 


11.86 


38.15 


12.03 


38.10 


12.19 


40 
41 


39.21 


11.99 


39.16 


12.16 


39.10 


12.33 


39.05 


12.50 


42 


40.16 


12.28 


40.11 


12.45 


40.06 


12.63 


40.00 


12.80 


42 


43 


41.12 


1 12.57 


41.07 


12.75 


41.01 


12.93 


40.95 


13.11 


43 


44 ,42.08 


12.86 


42.02 


13.05 


41.96 


13.23 


41.91 


13.41 


44 


45 


43.03 


! 13.16 


42.98 


13.34 


42.92 


13.53 


42.86 


13.72 


45 


46 


13.99 


: 13.45 


43.93 


13.64 


43.87 


13.83 


43.81 


14.02 


46 


47 


,44.95 


1 18.74 


44.89 


13.94 


44.82 


14.13 


44.76 


14,33 


47 


48 


145.90 


: 14.03 


45.84 


14.23 


45.78 


14.43 


45.71 


14 63 


48 


49 


146.86 


14.33 


46.80 


14.. 53 


46.73 


14.73 


46.67 


14.94 


49 


50 

*f5 


47.82 


14.62 


47.75 
Dep. 


14.83 


47.69 


15.04 
Lat. 


47.62 


15.24 


50 

■J 


Dap. 


Lat. 


Lat. 


Dep. 


Dep. 


Lat. 


73 


Deg. 


721 


Deg. 


72| 


Deg. 


72i Deg. 



TRAVERSE TABLE. 



107 



o 

P 
P 

'51 


1 
17 Deg. 1 

] 


in Deg. 1 

1 


17A Dfcg. 


171 De.. 




3 


Lat. 


Dep. 

14.91 1 


Laf.. 
48.71 


Dep. 


Lat. 


Dep. \ 


Lat. Dep. 


48.77 


15.12 


48.64 


15.34 1 


48.57 15.55 


51 


52 


49.73 ' 


15.20 


49.66 15.42 


49.59 


15.64 


49.52 15.85 


52 


53 


50.68 


15.50 


50.62 : 15.72 


50.55 


15.91 


50.48 16.16 5^ 


5i 


51.64 


15.79; 


51.57 j 16.01 


51.50 


16.24 1 


51.43 16.46 54 


55 


52.60 


16.08 '■ 


.52.53 I 16.31 


.52.45 1 16.54 


52.38 16.7?! 55 


56 


53.55 


16.37 


53.48 ; 16.61 


53.41 


16.84 1.53.33 17.07, 56 1 


57 


54.51 


16.67 


.54.44 16.90 


.54.36 


17.14 


54.29 


17.33 i 57 1 


58 


.55.47 


16.96 


55.39 ; 17.20 


55.32 


17.44 


55.24 


17.68 


58 


59 


56.42 


17.25 


56.35 17.50 


56.27 


17.74 


56.10 


17.99 


59 


60 
61 


57.38 
58.33 


17.54 1 


57.30 i 17.79 


57.22 


18.04 


5?'.]4 
53.10 


18.29 


60 


17.83 


58.26 . 18.09 


58.18 1 18,34 


18.60! 61 


62 


59.29 


18.13 1 


59.21 13.39 j 


59.13 18.64 


59.05 


18.90 j 62 


63 


60.25 


18.42' 


60.17 • 18.68 


60.08 18.94 


60.00 


19.21 


63 


64 


61.20 


18.71 


61.12 18.98 1 


61.04 19.25^ 


60.95 


19.51 


64 


65 


62.16 


19.00 


62.08 19.28 


61.99 : 19.55 


01.91 


19.82 


65 


66 


63.12 


19.30 


63.03 19.57 


62.95 i 19.35" 


62.86 


20.12 


66 


67 


64.07 


19.59 


63.99 19.87 


63.90 120.15 


63.81 


20.43 


67 


6S 


65.03 


19.88 


64.94 120.16 ' 


64.85! 20.45 


64.76 


20.73 68 


69 


65.99 


20.17 


65.90 120.46 | 


65.81 20.75 


65.72 


21.04 69 


70 
71 


6'S . 94 
67.90 


20.47 


68.85 120.75 ! 
67.81 1 21.05 1 


66.76 21.05 1 
67.71 121.35, 


66.67 


21. .34! 70 


20.76 


67.62 


21.65 71 


72 


68.85 


21.05 


63.76 21.35 


68.67 21.65! 


63.57 


21.95 72 


73 


69.81 


21.34 


69.72 121.65 


69.62 121.95 1 


69.52 


22.26 73 


74 


70.77 


21.64 


70.67 121.94 


70.58 


22.25 ; 


70.43 


22.56 74 


75 


71.72 


21.93 


71.63 [22.24 


71.53 


22.55 


71.43 


22.86 75 


76 


72.68 


22.22 


72.58 22.54 


72.43 


22.85 


72.33 


23.17 78 


77 


73.64 


22.51 


73.54 22.83 


1 73.44 


23.15 


73.33 


23.47 77 


78 


74.59 


22.80 


74.49 


23.13 


74.39 


23.46 


74.29 


23.78 78 


79 


75.55 


23.10 


75.45 


23.43 


75.34 


23.76 


75.24 


24.03 79 


80 


76.50 


23.39 


76.40 


23.72 


76.30 


24.06 


76.19 


24.39 1 80 


81 


77.46 


23.68 


; 77.36 


24.02 


77.25 


24.36 


77.14 124.69 | 81 


&2 


78.42 


23.97 


78.31 


24.32 


78.20 


24.66 


78.10 25.00 1 82 


83 


79.37 


24.27 


1 79.27 


24.61 


79.16 


25.96 


179.05 1 25.30 1 83 


84 


80.33 ! 24.56 


180.22 


24.91 


80.11 


25.26 


80.00 25.61 1 84 


85 


81.29 


24.85 


.81.18 


25.21 


81.07-25.56 


80.95! 25.91 | 85 


86 


82.24 


25.14 


82.13 


25.50 


82.02 25.86 


81.91 


26.22 i 86 


87 


83.20 


25.44 


183.09 


25.80 


82.97 26.16 
83.93 26.46 
84.88 26.76 


82.86 


26.52 87 


88 


84.15 


25.73 


184.04 


26.10 


83.81 


26.83 88 


89 


35.11 


26.02!! 85.00 


26.39 


i 84.76 


27.13 89 


■ 90 
91 


86.97 
87.02 


26.31 
126.61 


i 85.95 


26.69 
26.99 


'85.83 27.06 
86.79:27.36 


[85.72 
1 86.67 


27.44 1 90 


186.91 


27.74 1 91 


92 


1 87 98 


1 26.90 1 87.86 


27.28 


87.'?'4| 27.66 


87.62 28.05 1 92 


'.i2 


'88.94 


127.19 i 88.82 


27.58 


88.70 27.97 


188.57 2?. 35! 93 


94 


89.89 


27.48 89.77 


27.87 


89.65 28.27 


89.53 i 23.66 94 


95 


190.85 


27.78 1 90.73 


23.17 


90.60 28. ,57 


190.48 28.96 1 95 


96 


■91 8! 


28.07 1191.63 


28.47 


91.56 28.87 


; 91.43 29.27 1 96 


97 


i 92.7c 23.36 Ij 92.64 


23.76 


192.51 29.17 


192.33 29.57! 97 


98 


'93.72 


28.65 93.59 


29.06 


'93.46 29.47 


i 93.33 29.88 ! 9S 


99 94.67 


28.94 ij 94.55 


29.36 


94.42 29.77 


94.29 30.18 i 99 


100 


|^.63_ 


29.24 !|i)5. 50 


29.65 


95.37 30.07 


95.24 30.49 100 


6 

c 


Dep. 


Lat. 


Dop. 


i Lat. 


Dep. 1 Lat. 


\ Dep. Lat. 


c 

ci 


73 Deg. 

i 


1 

72| Deg. 


72^ Deg. 


72i Deg. 



108 



TRAVERSE TABLE. 



5 


18 


Deg. 


m 


Derr. 


1 

1 18^ Deg. 


181 Deg. 


^ 


p 






1 








,' tr 




Lat. 


Dep. 


Lat. 


1 Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


r3 

? 


1 


"0:95" 


0.31 


0.95 


0.31 


0.95 


0.32 


0.95 


0.32 


1 


2 


].90 


0.62 


1.90 


0.63 


1.90 


0.63 


1.89 


0.6i 


1 * 


3 


2.85 


0.93 


2.85 


0.94 


2 84 


0.95 


2.84 


0.96 


3 


4 


3.80 


1.24 


3.80 


1.25 


3 79 


1.2? 


3.79 


1 29 


i 4 


5 


4.76 


J.. 55 


4.75 


1.57 


4.74 


1.59 


4.73 


1.61 


' 5 : 


6 


5.71 


1.85 


5.70 


1.88 


5.69 


1.90 


5.68 


1.93 


6 J 


7 


6.66 


2.16 


6.65 


2.19 


6.64 


2.22 


6.63 


2.25 


7 


8 


7.61 


2.47 


7.60 


2.51 


7.59 


2.54 


7.58 


2.r-7 8 


9 


8.56 


2.78 


i S.55 


2.82 


8.53 


2.86 


8.52 


2.89 1 9 


10 


9.51 


3.09 


9.50 


3.13 


9.48 3.17 


9.47 


3.21 


10 


11 


10 ,46 


3.40 


16.45 


3.44 


10.43 1 3.49 


10.42 


" 3.54" 


fl 


12 


11.41 


3.71 


11.40 


3.76 


11.38 i J 81 


11.36 


3.86 


12 


13 


12.36 


4 02 


12.35 


4.07 


12.33 4 12 


12.31 


4.18 


13 


14 


13.31 


4 33 


13.30 


4.38 


13.28 4.4il|13.26 


4.. 50 


14 


15 


14.27 


4.64 


14.25 


4.70 


14.22 ; 4.76 :■ 14.20 


4.82 


15 


16 


15.22 


4.94. 


15.20 


5.01 


15.17 1 5.08 1: 15.15 


5.14 


16 * 


17 


16.17 


5.25 


16.14 


5.32 


16.12 


5.39 


, 16.10 


5.46 


17 


18 


17.12 


5.56 


17.09 


5.64 


17.07 


5.71 


1 17.04 


5.79 


18 i 


19 


18.07 


5.87 


18.04 


5.95 


18.02 


6.03 ! 17.99 


6.11 


19 i 


20 
21 


19.02 


6.18 


]'3 99 


6.26 


18.97 


6.35 


i 18.94 
19.89" 


6.43 ; 20 
6.75 i 21 


19.97 


6.49 


19.94 


6.58 


19.91 


6.66 


22 


20.92 


6.80 


20.89 


6.89 


20.86 


6.98 120.83 i 7.07 [ 22 I 


23 


21.87 


7.11 |21.84 


7.20 


21.81 


7.30 i 21.78 


7.39 ! 23 


24 '22.83 


7.42 i 22.79 


7.52 


22.76 


7.62! 22.7.3 


7 71 24 


25 


23.78 


7.73 23.74 


7.83i 


23.71 


7.93 1 23.67 


8.04 ' 25 


26 


24.73 


8.03 24.69 


8.14 


2^1.66 


8.25 24.62 


8.36 26 


27 


25.68 


8.34 25.64 


8.46 


25.60 


8.57 25.57 


8. 68 27 


28 


26.63 


8.65 1 26.59 


8.77 


26.55 


8.88 26.51 


9.00 28 


29 


27.. 58 


8.9^1 


27.54 


9.08 


27.50 


9.20 1 27.46 


9.32 


£9 


30 
3J 


28.53 


9.27| 


28.49 
29.44 


9.39 


28.45 


9.52 
9.84 


28.41 


9.64 


30 


29.48 


9.58 


9.71 


29.40 


29.35 


9.96 


Ml 


32 


30.43 


9.89 


30.39 


10.02 


30.35 


10.15 1 30.30 


10.29 


32 


33 


31.38 


10.20 


31.34 


10.33 


31.29 


10.47 


31.25 


10.61 


S3 


34 


.32.34 


10.61 


32.29 


10.65 


32.24 


10.79 


32.20 


10.93 


34 


35 


33.29 


10.82 


33.24 


10.96 


33.19 


11.11 


.33.14 


11.25 


35 


36 


34.24 


11.12 


34.19 


11.27 


.34.14 


11.42 


134.09 


11.57 


36 


37 


35.19 


11.43 


35.14 


11.59 


35.09 


11.74 


35.04 


11.89 


37 


38 


36.14 


11.74 


36.09 


11.90 


36.04 


12.06 


35.98 


12.21 


38 


39 


37.09 


12.05 


37.04 


12.21 


38.98 


12.37 


36.93 


12.54 


39 


40 


38.04 


12.36 


37.99 


12.53 


.37.93 


12.69 
13.01 


37.88 

38.82 


12.86 
13.18 


40 
41 


41 138.99 


12.67 


38.94 


12.84 


38.88 


42 39.94 


12.98 


39.89 


13.15 


39.83 


13.33 


39.77 


13.50 


42 


43 '40.90 


13.29 


40.84 


13.47 


40.78 


13 64 


40.72 


13.82 


43 


44 41.85 


13.60 


41.79 


13.78 


41.73 13.96 


41.66 


14.14 


44 


45 42.80 


13.91 


42.74 


14.09 


42.67 1 U.28 


42.61 


14.40 


45 


40 43.75 


14.21 


43.69 


14.41 


43.62 14.60 


43.56 


14.79 


46 


47 44.70 


14.. 52 


44.64 


14.72 


44.57 1 14.91 


44.51 


15.11 


47 


18 45.65 


14.83 


45.59 


15.03 


45.52 15,23 


45.45 


15.43 


48 


19 46.60 


15.14 


46.54 


15.35 


46.47 1 15.55 1 


46.40 


15.75 


49 


51) 47.55 
g ; Dep. 


15.45 
Lat. 

)eg. 


47.48 


J^5 , 6 6_ 


47.42 15.87! 


47.35 
Dep. 


16.07 
La.. 


_50 




1 


Dep. 

•''11 


Lai. 
Deg. 


Dep. 


Lat. 

1 


.1 


72 1 


7H Deg. 


7U Deg. 



TItAVETlSE TAI5LK 



109 



v3? 
p 
? 


18 Deg. 


m Deg. 


1 

l«i Deg. 


181 Deg. 


7 


Lat. ! Dep. 


Lat. 


Dep. 


j Lat. 1 Dep. 


1 Lat. Dep. 


i 


51 


i8.50 15.76' 


48.43 


15.97 .48.36 116.18 


48729^116739 


51 


52 


49.45 16.07 1 


49.33 


16.23 49.31 1 16.50 


49.24 '16 71 52 


53 


50.41 16.38 j 


50.33 


16.60 50.26 i 16.82 


50,19 17.04 53 


54 


51.36 16.69 


51.23 


16.91 51.21)17.13 


51.13 17.36 54 


65 


52.31 17.00 


52.23 


17.22 52.16 . 17.45 


52.03 117.08 oF. 


56 


53.28 17.30 i 


53.13 


17. .54 53.11 17.77, 


53.03 ; 18.00 56 


57 


.54.21 ; 17.61 1 


54.13 


17.85 i 54.05 ; 18.09 I 


53.93 113.32 57 


53 


55.10 1 17.92 


55.08 


18.16 55.00 : 18.40; 


54.92 i 18.6-i ' 53 


59 


.56.11 !l8.23 


53.03 


18.48 55.95 18.72 ^ 


55.87 1 18.96 ■ 59 


GO 

61 


57.06 1 18.541 


36.93 


18.79 


.56.90 19.04 1 


56.82 ! 19.29 


60 i 


58.01 i 18 85 ! 


57.93 1 19.10 


57.85 19.36 


57.76 19.61 


'61 


62 


.58.97 10.16 


53.68 j 19.42 


58.80 ! 19.67 


58.71 19.93 62 


63 


59.92 19.47 1 


59.83 1 19.73 


59.74 ; 19.99 


59.66 20.25 : 63 


61 


60.87: 19.78 


60.73 1 20.04 


60.69 20.31 


60.60 : 20.57 i G4 


65 


61.82 ' 20.09 


61.73 1 20.36 


61.64 20.62 1 


61.55 120.89 65 


66 


62.77 20.40 


62.68 i 20.67 


62.59 120.94: 


62.50 


21.22 : 66 


67 


63.72 20.70 


63.63 


20.98 i! 63.54 121.26 


63.44 


21.54 67 


68 


64.67 21.01 


64.58 


21. .30 


64.49 


21.53 


64.39 


21.86 1 63 


69 


65.62 21.32 


65.53 


21.61 


65.43 


21.89' 


65.34 122.13 . 69 


70 
71 


66.57; 21.63 


66.43 


21.92 


66.33 


22.21 


66.29 j 22.50 : 70 
67.23 122.82 : 71 


67.53 21.94 


67.43 


22.23 


67.33 


22.53 


72 


63.48 122.25 


63.38 


22.55 


68.28 


22.85 


68.18 123.14 , 72 


73 


69.43 i 22.56 i 


69.. 33 


22.86 


69.23 


23.16 


69.13 23.47 i 73 


74 


70. 3S ! 22.87 


70.28 


23.17 


70.18 


23.48 


70.07 123.79 74 


75 


71.33 i 23.18 


71.23 


23.49 


71.12 


23.80 


71.02 


24.11 75 j 


76 


72.28 i 23.49 


72.18 


23.80 


72.07 


24.12 


71.97 


24.43 


76 


77 


73 23 '23.79 


73.13 


24.11 1 


73.02 


24.43 i 


72.91 


24.75 


77 


78 


74.18 


24.10 174.03 


24.43 i 


73.97 


24.75 I 


73.86 


25.07 


78 


79 


75.13 


24.41 175.03 


24.74! 


74.92 


25.07 


74.81 


25.39 ' 79 


80 
81 


76.08 
77.04 


24.72! 
25.03 1 


75.98 


25.05 i 


75.87 


25.33 : 


75.75 


25.72: SO 


76.93 


25.37! 


76.81 125.70 


76.70 


26.04 81 


82 


77.99 


25.34 177.88 


25.68' 


77.76 126.02 


77.65 


26.36 82 


83 


78.94' 25.65 !| 78.83 


25.99 


78.71 


26.34 


78.60 


26.68 , S3 


84 


79.89; 25.96 !| 79.77 


26.31 


79.66 


26.65: 


79.54 


27.00 ; 84 


85 


80.84; 26.27 li 80.72 


28.62 


80.61 


26.97 


80.49 


27.32 ' 85 


86 


81.79, 26.58 !|81. 67 


26.93 i 


81.56 


27.29 , 


81. M 


27.64 86 


87 


82.74! 26.88 j 82.62 


27.25 1 


82.50 


27.61 


82.33 


27.97; &7i 


88 


83.69 ! 27.19 1 83.57 i 27.56 i 


83.45 


27.92 


83.33 


28.29 i 88 1 


89 


84.64: 27.50 


184.52 '27.87! 


84.40 1 23.24 


84.23 


28.61 ! S9e 


90 
91 


85.60; 27.81 ! 


85.47,23.18! 


85.35 123.56 , 


85.22 


28.93 


90 


86.55 128.12 1 


86.42 1 23.50: 


86.30 123.87: 


86.17 


29.25 


91 


92 


87.50 128.43 I 


87.37 28.81 1 


87.25 : 29.19 


87.12 


29.57 I 92 


93 


88.45 128.74 1 


88.32 29.12; 


88.19 29.51 


88.06 


29.89 ! 93 


94 


89.40 129.05 


89.27 1 29.441 


89.14.29.83 


89.01 


30.22 ! 94 


95 


90.35 '29.36 


90.22 29.75! 


90.09 30.14 


89.96 


30.54 95 


96 


91.30 29.67 


91.171 30.06 


91.04 30.46. 


b0.91 


30.86 96 


97 


92.25 29.97 


92.12 1 30.38 i 91.99 30.78 


91.85 1 31.13 97 


93 


93.20 30.28 


93.07| 30.69 ' 92.94 31.101 


92.80 131.50 9.:^ 


99 


94.15, 30.59 


94.02 31.00 ; 93.88 31.41 1 


93.75 131.82 99 


IOC 

c 

s 


95.11 i 30.90 


94.97 1 31.32 j 94.83 131.73 


94.69 132 14 


.00 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. ! Lat. | 


Dep. 


Lat. 


"i 


72 Deg. 


711 Deg. 


'H 


Deg. 


TH Deg. 


.a 

Q 



110 



TRAVFRSE TABLE. 



ST 

9 
o 
o 


19 Deg. 


m Deg. 


1 

19^ 


Deg. 


1 

191 Deg. 


» 

fD 


Lat. 


Dep. 
0.33 


Lat. 


Dep. 
0.33 


Lat. 


Dep. 


Lat. 
0.94 


Dep. 
0,34 


1 , 0.95 


0.94 


0.94 


0.33 


2l 1.89 


0.65 


1.89 


0.66 


1.89 


0.67 


1.88 


0.68 


2 


2 2.84 


0.98 


2.83 


0.99 


2.83 


l.UO 


2 82 


1.01 


3 


4 ; 3.78 


1.30 


3.78 


1.32 


3.77 


1.34 


3.76 


I 35 


4 


6 


4.73 


1.63 


4.72 


1.65 


4.71 


1.67 


4.71 


1.69 


5 


6 


6.67 


1.95 


5.66 


1.98 


5.66 


2.00 


5.65 


2.03 


8 


7 


6.62 


2.28 


6.01 


2.51 


6.60 


2.34 


6.59 


2.37 


7 


8 


7.56 


2.60 


7.55 


2.64 


7.54 


2.67 


7.53 


2.70 


8 


9 


8.51 


2.93 


8.50 


2.97 


8.48 


3.00 


8.47 


3.04 


9 


10 


9.46 


3.26 


9.44 
"10.38 


3.30 


9.43 


3.34 


9.41 


3.. 38 
3.72 


10 
~11 


11 


10.40 


3.58 


3.63 


10.37 


3.67 


10.35 


13 


11.35 


3.91 


11.33 


3.96 


11.31 


4.01 


11.29 


4.06 


12 


13 


12.29 


4.23 


12.27 


4.29 


12.25 


4.34 


12.24 


4.39 


13 


14 


13.24 


4.56 


13.22 


4.62 


13.20 


4.67 


13 18 


4.73 


14 


15 


14.18 


4.88 


14.16 


4.95 


14.14 


5.01 


14.12 


5.07 


15 


16 


15.13 


5.21 


15.11 


5.28 


15.08 


5.34 


15. oe 


5.41 


16 


17 


16.07 


5.. 53 


16.05 


5.00 


16.02 


5.67 


16 00 


5.74 


17 


18 


17.02 


5.86 


16.99 


5.93 


10.97 


6.01 j 


16.94 


6.08 


18 


19 


17.96 


6.19 


17.94 


6.26 


17.91 


6.34 


17.88 


6.42 


19 


20 


18.91 


6.51 


18.88 


6.59 


18.85 
19.80' 


6.68 1 


18.82 
19.76 


6.70 
7.10 


20 
21 


21 


19.86 


6T84 


19.83 


6.92 


7.011 


22 


20.80 


7.16 


20.77 


7.25 , 


20.74 


7.34 1 


20.71 


7.43 


22 


23 


21.75 


7.49 


21.71 


7.58 


21.68 


7.68, 


21.05 


7.77 


23 


24 


22.69 


7.81 


22.66 


7.91 


22.62 


8.01 


22.59 


8.11 


24 


25 


23.64 


8.14 


23.60 


8.24 


23.57 


8.35 


23.53 


8.45 


25 


26 


24.58 


8.46 


24.55 


8.57 


24.51 


8.68 


24.47 


8.79 


26 


27 


25.53 


8.79 


25.49 


8.90 


25.45 


9.01 


25.41 


9.12 


27 


28 


26.47 


9.12 


26.43 


9.23 I 


26.39 


9.35 


26.35 


9.46 


28 


29 


27.42 


9.44 


27.38 


9.56 ! 


27.34 


9.08 


27.29 


9.80 


29 


30 
31' 


28.37 
29.31 


9.77 
10.09 


28.32 


9.89 


28.28 


10.01 j 


28.24 
29.18 


11/.14 
10 48 


30 
3i 


29.27 


10.22! 


29.22 


10.35 1 


32 


30.26 


10.42 


30.21 


10.55 1 


30.16 


10.68 


30.12 


10 81 


32 


33 


31.20 


10.74 


31.15 


10.88 


31.11 


11. 02, 


31.06 


11 15 


33 


34 


32.15 


J1.07 


32.10 


11.21 ! 


32.05 


11.35: 


33.00 


11 49 


34 


35 


33.09 


11.39 


33.04 


11.54i 


32.99 


11.68 1 


32.94 


11.83 


35 


36 


34.04 


11.72 


33.99 


11.87 


33.94 


12.02! 


33.88 


12.17 


36 


37 


34.98 


12.05 


34.93 


12.20 


34.88 


12.35 i 


34.82 


12.50 


37 


38 


35.93 


12.37 


35.88 


12.53 


35.82 


12.68 


35.76 


12.84 


33 


39 


36.88 


12.70 


36.82 


12.86 


36.76 


13.02 


36.71 


13.18 


39 


40 
4f 


37.82 


13.02 


37.76 
38.71 


13.19 


37.71 


13.35 


37.65 


13.52 

13.8:^ 


40 
'41 


38.77 


13.35 


13.52 


38.05 


13:69 


38.59 


42 


39.71 


13.67 


39.65 


13.85 


39.59 


14.02 ! 


39.53 


14.19 


42 


43 


40,66 


14.00 


40.60 


14. :d 


40.53 


14.35 i; 40.47 


14.5:5 


43 


44 


41.60 


14.32 


41.54 


14.51 


41.48 


14.69 


41.41 


14.87 


44 


45 


42.55 


14.65 


42.48 


14.84 


42.42 


15. Of; 


42.35 


15.21 


45 


46 


43.49 


14.98 


43.43 


15.17 


43.36 


15.33 


43.29 


15.. 54 


46 


47 


44.14 


15.30 


44.37 


15.. 50 


44.30 


15.69 1 


44.24 


15.SS 


47 


48 


45.38 


15.63 


45.32 


15.83 1 


45.25 


16.02 : 


45.18 


16.22 


48 


49 


46.33 


15.95 


46.26 


16.15} 


46.19 


16.36 


46.12 


16.56 


49 


50 


47.28 


16.28 


47.20 


16.48 


47.13 


16.89 
La. 


47.06 
Dep. 


1.0.90 
Lhi. 


50 

§ 

l! 


I 

CO 

5 


Dep. 

711 


Lat. 


Dep. 


Lat. 


Dep. 


701 


1 
De?. 


70,: 


>8- 


70.1 Deg. 



TRAVERSE TABLE. 



Ill 



"51 


19 Deg. 


191 Deg. 

1 


19A Deg. 


19| Deg. 


"51 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


48.22 


16.60 


48.15 


16.81 


48.07 


17.02 


48.00 


17.23 


52 49.17 


16.93 


49.09 


17.14 


49.02 


17.30 


48.94 


17.57 


52 


5:j 


50.11 


17.26 


50.04 17.47 j 


49.96 17.69 1 


49.88 


17.91 


53 


54 


51.06 


17.58 


50.98 1 17.80 1 


50.90 


18.03 


.50.82 


18.25 


54 


55 


52.00 


17.91 


51.92 18.13 1 


51.85 


18.36 


51.76 


18.. 59 


55 


56 


52.95 


18.23 


52.87 


18.46 


.52.79 


18.69 


52.71 


18.92 


56 


57 


53.89 


18.56 1 


53.81 


18.79 


53.73 


19.03 


53.65 


19.26 


57 


58 


54.84 


18.88 


54.76 


19.12 


54.67 


19.36 


54.59 


19.00 


58 


59 


55.79 


19.21 


55.70 


19.45 


55.62 


19.69 


55.53 


19.94 


59 


60 
61 


50.73 19.53 1 


56.65 


19.78 


56.56 
57.50 


20.03 
20.86 


56.47 


20.27 


00 
61 


57.68 


19.86 


57.59 


20.11 


.57.41 


20.61 


62 


58.62 


20.19 


58.53 


20.44 


58.44 


20.70 


58.35 


20.95 


62 


63 


59.57 


20.51 


59.48 


20.77 


59.39 


21.03 


59.29 


21.29 


63- 


64 


60.51 


20.84 


60.42 


21.10 


60.33 


21.36 


60.24 


21.63 


64 


65 


61.46 


21.16 


61.37 


21.43 


01.27 


21.70 


61.18 


21.96 


65 


66 


02.40 


21.49 


62.31 


21.76 


62.21 


22.03 


62.12 


22.30 


66 


67 


63.35 


21.81 


63.25 


22.09 


63.16 


22.37 


63.06 


22.64 


67 


68 


64.30 


22.14 


64.20 


22.42 


64.10 


22.70 


64.00 


22.93 


68 


69 


65.24 


22.40 


65.14 


22.75 


65.04 


23.03 


64.94 


23.32 


69 


70 
71 


66.19 


22.79 


66.09 


23.08 


65.98 


23.37 


65.88 


23.65 


70 
71 


67.13 


23.12 


67.03 


23.41 


66.93 


23.70 


68.82 


23.99 


72 


08.08 


23.44 


67.97 


23.74 


67.87 


24.03 


67.76 


24.33 


72 


73 


69.02 


23.77 


68.92 


24.07 


68.81 


24.37 


68.71 


24.67 


73 


74 


69.97 


24.09 


69.86 


24.40 


69.76 


24.70 


69.65 


25.01 


74 


75 


70.91 


24.42 


70.81 


24.73 


70.70 


25.04 


70.59 


25.34 


75 


76 


71.86 


24.74 


71.75 


25.06 


71.64 


25.37 


71.53 


25.68 


76 


77 


72.80 


25.07 


72.69 


25.39 


72.58 


25.70 


72.47 


26.02 


77 


78 


73.75 


25.39 


73.64 


25.72 


73.53 


26.04 


73.41 


26.36 


78 


79 


74.70 


25.72 


74.58 


26.05 


74.47 


26.37 


74.35 


26.70 


79 


80 
81 


75.64 


26.05 


75.53 


26.. 38 


75.41 
76.35 


26.70 
27.04 


75.29 
76.24 


27.03 


80 

81 


76.59 


26.37 


76.47 


26.70 


27.37 


82 


77.53 


26.70 


77.42 


27.03 


77.30 


27.37 


77.18 


27.71 


82 


83 


78.48 


27.02 


78.36 


27.36 


78.24 


27.71 


78.12 


28.05 


83 


84 


79.42 127.35 


79.30 


27.69 


79.18 


23.04 


79.06 


28.39 


84 


85 


80.37 


27.67 


80.25 


28.02 


80.12 


28.37 


80.00 


28.72 


85 


86 


81.31 


23.00 


81.19 


28.35 


81.07 


28.71 


80.94 


29.06 


86 


87 


82.26 


28.32 


82.14 


28.68 


82.01 


29.04 


81.88 


29.40 


87 


88 


8.3.21 


28.65 


83.08 


29.01 


92.95 


29.37 


82.82 


29.74 


88 


89 


84.15 


28.98 


84.02 


29.34 


83.90 


29.71 


83.76 


30.07 


89 


90 
91 


85.10 
86.04 


29.30 


84.97 


29.67 


84.84 1 30.04 


84.71 


30.41 


90 
91 


29.63 


85.91 


30.00 


85.78 


30.38 


85.65 


30.75 


92 


86.99 29.95 


86.86 


30.33 


86.72 


30.71 


86.59 


31.09 


92 


93 


87.93,3(J.28 


87.80 


30.66 


87.67 


31.04 


87.53 


31 .43 


93 


94 


88.88 1 30.60 


88.74 


30.99 


88.61 


31.38 


88.47 


31.76 


94 


95 


89.82 i 30.93 


89.69 


31.32 


89.55 


31.71 


89.41 


32.10 


95 


96 


90.77 1 31.25 


90.63 


31.65 


90.49 


32.05 


90.35 


32.44 


96 


97 


91.72 31.58 


91.58 


31.98 


91.44 


32.38 


91.29 


32.78 


97 


98 


92.66 31.91 


92.. 52 


32.31 


92.38 


32.71 


92.24 


33.12 


98 


99 


93.61 


32.23 


93.46 


32.64 


93.32 


33.05 


93.18 


33.45 


99 


IOC 


04.55 


32.56 


94.41 


32.97 


94.26 


33.38 


94.12 
Dep. 


33.79 


100 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Lat. 


71 Deg. 


701 Deg. 


70J Veg. 


70i Deg. 



112 



TRAVERSr T.\nT,E. 



1 

c 

3 

? 

" 1 


20 Deg. 


20i Deg. 


20 1 


Deg. 


201 


Deg. 


1 


Lat. 

0.94 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

o^T 


0.34 


0.94 


0..35 


0.94 


0.35 


0.94 


2 


1.88 


0.68 


1.88 


0.69 


1.87 


0.70 


1.87 


0.71 


2 


3 


2.82 


1.03 


2.81 


1.04 


2.81 


1.05 


2.81 


1.06 


3 


4 


3.76 


1.37 


3.75 


1.38 


3.75 


1.40 


3.74 


1.42 


i 


5 


4.70 


1.71 


4.69 


1.73 


4.68 


1.75 


4.68 


1.77 


5 


G 


5.64 


2.05 


5.63 


2.08 


5.62 


2.10 


5.61 


2.13 


6 


7 


6.58 


2.39 


6.57 


2.42 


6.56 


2.45 


6.55 


2.48 


7 


8 


7.52 


2.74 


7.51 


2.77 


7.49 


2.80 


7.48 


2.83 


6 


9 


8.46 


3.08 


8.44 


3.12 


8.43 


3.15 


8.42 


3.19 


9 


10 

11 


9.40 


3.42 


9.38 
10.32 


3.46 

3.81 


9.37 
10.30 


3.50 


9.35 


3.54 


lO 

~11 


10.34 


3.76 


3.85 


10.29 


3.90 


13 1 11.28 


4.10 


11.26 


4.15 


11.24 


4.20 


11.22 


4.25 


12 


13 


12.22 


4.45 


12.20 


4.50 


12.18 


4.55 


12.10 


4.61 


13 


14 


13.16 


4.79 


13.13 


4.85 


13.11 


4.90 


13.09 


4.96 


14 


15 


14.10 


5.13 


14.07 


5.19 


14.05 


5.25 


14.03 


5.31 


15 


16 


15.04 


5.47 


15.01 


5.54 


14.99 


6.60 


14.96 


5.67 


16 


17 


15.97 


5.81 


15.95 


5.88 


15.92 


5.95 


15.90 


6.02 


17 


18 


16.91 


6.16 


16.89 


6.23 


16.86 


6.30 


16.83 


6.38 


18 


19 


17.85 


6.50 


17.83 


6.58 


17.80 


6.65 


17.77 


6.73 


19 


20 


18.79 


6.84 


18.76 


6.92 


18.73 


7.00 


18.70 


7.09 


20 
21 


21 


19.73 


7.18 


19.70 


7.27 


19.67 


7.35 


19.64 


7.44 


22 


20.67 


7.52 


20.64 


7.61 


20.61 


7.70 


20.57 


7.79 


'^2 


23 


21. C] 


7.87 


21.58 


7.96 


21.54 


8.05 


21.51 


8.15 


23 


24 


22.55 


8.21 


22.52 


8.31 


22.48 


8.40 


22.44 


8.50 


24 


25 


23.49 


8.55 


23.45 


8.65 


23.42 


8.76 


23.38 


8.86 


25 


26 


24.43 


8.89 


24.39 


9.00 


24.35 


9.11 


24.31 


9.21 


26 


27 


25.37 


9.23 


25.33 


9.35 


25.29 


9.46 


25.25 


9.57 


27 


28 


26.31 


9.68 


26.27 


9.69 


26.23 


9.81 


26.18 


9.92 


28 


29 


27.25 


9.92 


27.21 


10.04 


27.16 


10.16 


27.12 


10.27 


29 


30 


28.19 


10.26 


28.15 


10.38 


28.10 


10.51 


28.05 


10.63 


30 
'31 


31 


29.13 


10.60 


29.08 


10.73 


29.04 


10.86 


28.99 


10.98 


32 


30.07 


10.94 


30.02 


11.08 


29.97 


11.21 


29.92 


11.34 


32 


33 


31.01 


11.29 


30.96 


11.42 


30.91 


11.56 


30.86 


11.69 


33 


34 


31.95 


11.63 


31.90 


11.77 


31.85 


11.91 


31.79 


12.05 


34 


35 


32.89 


11.97 


32.84 


12.11 


32.78 


12.26 


32.73 


12.40 


35 


36 


33.83 


12.31 


33.77 


12.46 


33.72 


12.61 


33.66 


12.75 


36 


37 


34.77 


12.65 


34.71 


12.81 


34.66 


12.96 


34.60 


13.11 


37 


38 


35.71 


13.00 


35.65 


13.15 


35.59 


13.31 


35.54 


13.46 


38 


39 


36.65 


13.34 


36.59 


13.50 


36.53 


13.66 


36.47 


13.82 


39 


40 
41 


37.59 
38.53 


13.68 


37.53 


13.84 


37.47 


14.01 


37.41 


14.17 


40 
41 


14.02 


38.47 


14.19 


38.40 


14.36 


38.34 


14.53 


42 


39.47 


14.36 


39.40 


14.54 


39.34 


14.71 


39.28 


14.88 


42 


43 


40.41 


14.71 


40.34 


14.88 


40.28 


15.06 


40.21 


15.23 


43 


44 


41.35 


15.05 


41.28 


15.23 


41.21 


15.41 


41.15 


15.. 59 


44 


45 


42.29 


15.39 


42.22 


15.58 


42.15 


15.76 


42.08 


15.94 


45 


46 


43.23 


15.73 


43.16 


15.92 


43.09 


16.11 


43.02 


16. .30 


46 


47 


44.17 


16.07 


44.09 


16.27 


44.02 


16.46 


43.95 


16.65 


47 


48 45.11 


16.42 


45.03 


16.61 


44.96 


16.81 


44.89 


17.01 


48 


49 146.04 


16.76 


45.97 


16.96 


45.90 


17.16 


45.82 


17.36 


49 


50 

u 

c 


46.98 


17.10 


46.91 


17.31 


46.83 


17.51 


46.76 


17.71 


_50 

6 
o 

c 

d 




Dep. 


Lat. 


Dep. 

69| 


Lat. 
Deg. 


Dep. 


Lat. 


Dep. 


Lat. 


70 


Deg. 


69i Deg. 


69i 


Deg 



TRAVEKSE TABLE. 



113 



1 


20 Deg. 


20$ Deg. 


201 


Deg. 
Dep. 


201 Deg, 


Ci 

o 


3 
P 


Lat. Dep. 


Lat. Dep. 


Lat. 


Lat. 


Dep. 


51 


47.92 17.4-4 1 


47,35 1 17". 65 
43.79 1 18.00 1 


47.771 17.86 


47.69 


18.07 


51 


52 1 


43.86 


17.79 


48.711 18.211 


43.63 


18.42 


52 


53' 


49.80 


18.13 t 


49.72; 1S.34I 


49.64 i 13.56 49.56! 13.73 


53 


54 


50.74 18.47: 


50.06 18.69 1 


50.58 1 18.91 ! 50.50 1 19.13 ! 


54 


55 


51.63 


18.81 1 


51.60' 19.04^ 


51.52 i 19.26. 


51.43 


19.49 


55 


56 i 


52.62 


19.15 1 


52.54 


19.33 


52.45! 19.61 


52.37 


19.84 


56 


57 


53.56 


19.50 1 


53.48 1 


19.73, 


53.39! 19.96 


53.30 


20.19 


57 


5S 


54.50 


19.84 1 


54.42 


20.07 1 


54.33 ' 20.31 


54.24 


20.55 


53 


59 


55.44 


20.18' 


55.35 


20.42 i 


55.26 20.66 !l 55.17 


20.90 


59 


61 


56.33 


20.52 
20.86 i 


56.29 


20.77 i 


56.20 
57.14" 


21.011 56.11 


21.26 
21.61 


60 
61 


57.32 


57.23 


21.11 


21.36; 


57.04 


62 


58.26 


21.21 ' 


53.17 


21.46 


58.07 


21.71 ; 


57.93 


21.97 


62 


63 


59.20 1 21.55 1 
60.14121.89' 


59.11 


21.81 


59.01 


22.06 1 


58.91 


22.32 


63 


64 


60.04 


22.15 


59.95 


22.41 59.85 


22.67 


64 


65 


61.03 22.23 


60.93 


22.50 


60.88 


22.76 


60.73 23.03 


65 


66 


62.02 1 22.57 


61.92 


22.84; 


61.82 


23. Hi 


61.72 


23.33 


66 


67 


62.96: 22.92 


62.86 


23.19' 


62.76 


23.46; 


62.65 


23.74 


67 


6S 


63.90 23.26 


63.80 


23.54 1 


63.69 


23.81; 


63.59 


24.09 


68 


69 


64.84 23.60 


64.74 


23.88' 


6t.63 


24.16; 


64.52 


24.45 


69 


70 
71 


65.78 23.94 


65.67 24.23 


65.57 
66.50 


24.51 : 
24.86 


65.46 


24.80 


70 
71 


66.72 i 24.23 


65.61 


9A.57 


66.39 


25.15 


72 


67.66] 24.63 


67.55 


24.92 


67.44 


25.21 


67.33 


25. 5L 


73 


73 


68.60 i 24.97 


68.49 


25.27 


68.33 


25.57; 


63.26 


25.86 


73 


74 


69.54 j 25.31 ; 


69.43 


25.61 


69.31 


25.92 


69.20 


26.22 


74 


75 


70.48 25.65 


70.36 


25.96 1 


70.25 


26.27 


70.14 


26.57 


75 


76 


71.42 1 25.99 


71.30 


26.30 1 


71.19 


26.62 


71.07 


26.93 


76 


77 


72.36 1 26.34 


72.24 


26.65 


72.12 


26.97 


72.01 


27.23 


77 


78 


73.30 26.63 


73.18 


27.00 


73.06 


27.32 


72.94 


27.63 


73 


79 


74.24; 27.02 


74.12 


27.34 


74.00 


27.67 


73.83 


27.99 


79 


80 
81 


75.18 1 27.36; 
76.12 i 27.70 


75.06 


27.69 


74.93 


23.02 


174.81 


23.34 


80 
81 


75.99 1 28.04 


75.87 1 23.37 


75.75 


23.70 


82 


77.05 


23.05 


76.93 


28.33 


76.81 


28.72 


76.63 


29.05 


82 


S3 


77.99 


28.39 


77.87 


23.73 


77.74 


29.07 


77.62 


29.41 


83 


84 


73.93 


23.73 


78.81 


29.07 


78.68 


29.42 


73.55 


29.76 


84 


85 


79.87 i 29.07 


79.75 


29.42 


79.62 


29.77 


i 79.49 


30.11 


85 


86 


80.81 


29.41 


80.68 1 29.77 


80.55 


30.12 


80.42 


30.47 


86 


87 


81.75 


29.76 


81.62 30.11 


81.49 


30.47 


181.36 


30.82 


87 


88 


82.69 


30.10 


82.56 I 30.46 


82.43 


30.82 


182.29 


31.^18 


83 


89 


83.63 


30.44 


83.50 1 30.80 


83.36 


31.17 


83.23 


31.53 


89 


90 
91 


84.57 


30.73 


84.44 1 31.15 


84.30 


31.52 


184.16 


131.89 


90 
91 


185.51 1 31.12 


85.33 


31.50 


85.24 


31.87 


85.10 


32.24 


92 


! 86.45 i 31.47 


86.31 


31.84 


86.17 


32.22 


! 86.03 


32.59 


92 


93 


1 87.39 i 31.81 


1 87.25 


132.19 


87.11 


32.57 


! 86.97 


32.95 


93 


94 


83.33' 32.15 


83.19 , 32.54 


83.05 132.92 


! 87.90 


33.30 


94 


95 


89.27 32.49 


89.13' 32.83 


83.93 '33.27 


183.84 


33.65 


95 


96 


; 90.21 32.83 


90.07 


1 33.23 


89.92 33.62 


i 89.77 


34.01 


96 


97 


i 91.15! 33.18 


91.00 


33.57 


90.86 1 33.97 


190.71 


34.37 


97 


98 


92.09 33.52 


91.94 


33.92 


91.79 


34.32 


91.64 


.34.72 


9S 


99 


93.03 1 33.86 


92.88 


34.27 


92.73 


34.67 


92.58 


135.07 


1 99 


lOO 

1 


93.97; 34.20 


93.82! 34.61 


93.67 


35.02 


93.51 


35.43 


! 100 

11 


i Dep. 
70 


[ Lat. 


Dep. Lat. 


Dep. 1 Lat. 


Dep. 


Lat. 


Deg. 


69| Deg. 


69| Deg. 


69+ Deg 



114 



TRAVEJiSK TABLE. 



p 

3 
n 
o 


21 Deg. 


2U Deg. 


21 1 Deg. 


21| Deg. 


a 
1 


Lat. 
0.93 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.36 


0.93 


0.36 


0.93 


0.37 


0.93 


0.37 


2 


1.87 


0.72 


1.86 


0.72 


1.86 


0.73 


1.86 


0.74 


2 


3 


2.80 


1.08 


2.80 


1.09 


2.79 


1.10 


2.79 


1.11 


3 


i 


3.73 


1.43 


3.73 


1.45 


3.72 


1.47 


3.72 1 1.48 


4 


li 


4.67 


1.79 


4.66 


1.81 


4.65 


1.83 


4.64 


1.85 


5 


b 


5.60 


2.15 


5.59 


2.17 


5. 58 


2.20 


5.57 


2.22 


6 


V 


6.54 


2.51 


0.52 


2.54 


6.51 


2.57 


6.50 


2.59 


7 


8 


7.47 


2.8? 


7.46 


2.90 


7.44 


2.93 


7.43 


2.96 


8 


9 


8.40 


3.23 


8.39 


3.26 


8.37 


3.30 


8.36 


3.34 


9 


10 


9.34 


3.58 


9.32 


3.62 


9.30 


3.67 
4.03 


9.29 


3.71 
4.08 


10 
"ll 


11 


10.27 


3.94 


10.25 


3.99 


10.23 


10.22 


12 


11.20 


4.30 


11.18 


4.35 


11.17 


4.40 I 


11.15 


4.45 


12 


13 


12.14 


4.66 


12.12 


4.71 


12.10 


4.76 


12.07 


i.82 


13 


14 


13.07 


5.02 


13.05 


5.07 


13.03 


5.131 


13.00 


5.19 


14 


15 


14.00 


5.38 


13.93 


5.44 


13.96' 5.50 1 


13.93 


5.56 


15 


16 


14.94 


5.73 


14.91 


5.80 


1 14.89 


5.86 


14.86 


5.93 


16 


U 


15.87 


6.09 


15.84 


6.16 


15.82 


6.23 


15.79 


6.30 


17 


18 


16.80 


6.45 


16.78 


6.52 


i 16.75 


6.60 


16.72 


6.67 


18 


19 


17.74 


6.81 


17.71 


6.89 


17.68 


6.96 


17.65 


7.04 


19 


20 


18.67 


7.17 


18.64 


7.25 


18.01 


7.33 


18.58 1 7.41 


20 


21 


19.61 


7.53 ; 19.57 


7.61 


19.54 


7.70 


19.50 1 7.78 1 21 


22 


20.54 


7.88 1 20.50 


7.97 


20.47 


8.06 


20.43 1 8.15 22 


23 


21.47 


8.24 ; 21.44 


8.34 


21.40 


8.43 


21.36 8.52 23 


24 


22.41 


8.60 


22.37 


8.70 


22.33 


8.80 1 


22.29 


8.89 24 


25 


23.. 34 


8.96 


23.30 


9.06 


23.26 


9.16 


23.22 


9.26 25 


26 


24.27 


9.32 


24.23 


9.42 


24.19 9.53 i 


24.15 


9.63 26 


27 


25.21 


9.68 


25.16 


9.79 


25.12 1 9.90 ! 


25.08 


10.01 


27 


28 


26.14 


10.03 


26.10 


10.15 


26.05, 10.26 ! 


26.01 10 33 


28 


29 


27.07 


10.39 


27.03 


10.51 


26.98 ■: 10.63 


26.94 10.75 


29 


30 


28.01 


10.75 


27.90 


10.87 


27.91 : 11.00 


27.86 11.12 


30 


31 


28.94 


11.11 


28.89 


11.24 


28.84, 11.36 


28.79 


11.49 


31 


32 


29.87 


11.47 


29.82 


11. GO 


29.77 11.73 1 


29.72 


11.86 


32 


33 


30.81 


11.83 


30.76 


11.96 


30.70 12.09 


30.65 


12.23 


33 


34 


31.74 


12.18 


31.69 


12.32 


31.63 1 12.46 


31.58 


12.60 


34 


35 


32.68 


12.54 


32.62 


12.69 


32.58 i 12.83 


32.51 


12.97 


35 


36 


33.61 


12.90 


33.55 


13.05 


33.50: 13.19 


33.44 


13. .34 


36 


37 


34.54 


13.26 


34.48 


13.41 


34.43 1 13.56 


34.37 


13.71 


37 


38 


35.48 


13.62 


35.42 


13.77 


35.36 1 13.93 


35.29 


14.08 


38 


39 


36.41 


13.98 


36.35 


14.141 


36.29 14.29 


36.22 


14.45 


39 


40 
41 


37.34 


14.33 


37.28 


14.50 


37.22' 14.66 1 


37.15 


14.82 


40 
41 


38.28 


14.69 


33.21 


14.86 


38.15. 15.03 


38.08 1 15.19 


42 


39.21 


15.05 


39.14 


15.22 


39.08 i 15.39, 


39.01 15.56 


42 


43 


40.14 


15.41 


40.08 


15.58 


40.01 1 15.76 ' 


39.94 1 15.93 


43 


44 


41.08 


15.77 


41.01 


15.95 


40.94! 16.13' 


40.87 1 16.30 


44 


45 


42.01 


16.13 


41.94 


16.31 


41.87 i 16.49 


41.80 1 16.63 1 45 


46 


42.94 


16.48 


142.87 


16.67 


42.80! 16.86 


42.73! 17.05 1 46 


47 


43. S8 


16.84 


j 43.80 


17.03 


43.73: 17.23 


43.65 1 17.42 \ 47 


48 


44.81 


17.20 


144.74 


17.40 


44.66 i 17.59 


44.58 1 17.79 


48 


49 


45.75 


17.56 


145.67 


17.76 


45.59 17.96 


45.51 1 18.16 


49 


50 

.a 


46.63 


17.92 


146.60 


18.12 


48.52 18.33 


46.44 
Dep. 


18.53 


50 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. 


Lat. 


69 Deg. 


68| Degr 


68i Deg. 


en\ Deg. 



TJiAVERSE TABLE. 



115 



1 

5i 


21 Deg. 


21i Deg. 


21A Deg. 

1 


211 Deg. 


5' 


Lat. 


Dep. 1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. i 


47.61 


18.28 


47.53 


18.48 


47.45 


18.69 


47.37 


18>90 


51 


52 


48.55 18.64 1 


48.46 


18.85 


48.38 


19.06 


48.30 


19.27 


52/ 


53 


49.48 


18.99 


49.40 


19,21 


49.31 


19.42 


49.23 


19.64 


5;i 


64 


50.41 


19.35 


50.33 


19.57 


50.24 


19.79 


50.16 


20.01 


54 


55 


51 35 


19.71 


51.26 


19.93 


51.17 


20.16 


51.08 


20.38 


55 


56 


52 28 


20.07 


52.19 20.30 1 


52.10 


20.52 


52.01 


20.75 


.5f, 


5? 


53 2] 


20.43 


53.12 


20.66 


53.03 


20.89 


52.94 


21.12 


57 


58 


54.15 


20.79 


54.06 


21.02 


53.96 


21.26 


53.87 


21.49 


58 


59 


55.08 


21.14 


54.99 


21.38 


54.89 


21.62 


54.80 


21.86 


59 


60 
61 


56.01 


21.50 
21.86 


55.92 


21.75 


55.83 


21.99 


55.73 


22.23 


60 
61 


56.95 


56.85 


22.11 


56.76 


22.36 


56.66 


22.60 


62 


57.88 


22.22 


57.78 


22.47 


57.69 


22.72 


57.59 


22.97 


62 


63 


58.82 


22.58 


58.72 


22.83 


58.62 


23.09 


58.52 


23.35 


63 


64 


59.75 


22.94 


59.65 


23.20 


59.55 


23.40 


59.44 


23.72 


64 


65 


60.68 


23.29 


60.58 


23.56 


60.48 


23.82 


60.37 


24.09 


65 


60 


61.62 


23.65 


61.51 


23.92 


01.41 


24.19 


61.30 


24.46 


66 


67 


62.55 


24.01 


62.44 


24.28 


62.34 


24.56 


62.23 


24.83 


67 


68 


63.48 


24.37 


63.38 


24.65 


63.27 


24.92 


63.16 


25.20 


es 


69 


64.42 


24.73 


64.31 


25.01 


64.20 


25.29 


64.09 


25.57 


69 


70 
71 


65.35 


25.09! 


65.24 


25.37 


65.13 


25.66 


65.02 


25.94 


70 

71 


66.28 


25.44 


66.17 


25.73 


66.06 


26.02 


65.95 


26.31 


72 


67.22 


25.80 1 


67.10 


26.10 


66.99 


26.39 


66.87 


26.68 


72 


73 


68.15 


26.16 


68.04 


26.46 


67.92 


26.75 


67.80 


27.05 


73 


74 


69.08 


26.52 


68.97 


26.82 


68.85 


27.12 


68.73 


27.42 


74 


75 


70.02 


26. 8S 


69.90 


27.18 


69.78 


27.49 


69.66 


27.79 


75 


76 


70.95 


27.24 


70.83 


27.55 


70.71 


27.85 


70.59 


28.16 


76 


77 


71.89 


27.59 


71.76 


27.91 


71.64 


28.22 


71.52 


28.53 


77 


78 


72.82 


27.95 


72.70 


28.27 


72.57 


28.59 


72.45 


28.90 


78 


79 


73.75 


28.31 


73.63 


28.63 


73.50 


28.95 


73.38 


29.27 


79 


80 
81 


74.69 


28.67 


74.56 


29.00 


74.43 


29.32 


74.30 


29.64 


80 


75.62 


29.03 


75.49 


29.36 


75.36 


29.69 


75.23 


30.02 


81 


82 


76.55 


29.39 


76.42 


29.72 


76.29 


30.05 


76.16 


30.39 


82 


83 


77.49 


29.74 


77.36 


30.08 


77.22 


30.42 


77.09 


30.76 


83 


84 


78.42 


30.10 


78.29 


30.44 


78.16 


30.79 


78.02 


31.13 


84 


85 


79.35 


30.46 


79.22 


30.81 


79.09 


31.15 


78.95 


31.50 


85 


86 


80.29 


30.82 


80.15 


31.17 


80.02 


31.52 


79.88 


31.87 


86 


87 


81.22 


31.18 


81.08 


31.53 


80.95 


31.89 


80.81 


32.24 


87 


88 


82.16 


31 54 


82.02 


31.89 


81.88 


32.25 


81.74 


32.61 


88 


89 


83.09 


31.89 


82.95 


32.26 


82.81 


32.62 


82.66 


32.98 


89 


90 
91 


84.02 


32.25 


83.88 


32.62 


83.74 


32.99 


83.59 


33.35 


90 
91 


84.96 


32.61 


84.81 


32.98 


84.07 


33.35 


84.52 


33.72 


92 


85.89 


32.97 


85.74 


33.34 


85.60 


33.72 


85.45 


34.09 92 


93 


86.82 


33.33 


86.68 


33.71 


85.53 


34.08 


186.. 38 


34.46 93 


94 


87.76 


33.69 


87.61 


34.07 


87.46 


34.45 


87.31 


34.83 1 91 


95 


88.69 


34.04 


88.54 


34.43 


88.39 


34.82 


88.24 


35.20 95 


96 


89.02 


34.40 


89.47 


34.79 


89.32 


35.18 


89.17 


35.57 96 


97 


90.56 


34.76 


90.40 


35.16 


90.25 


35.55 


90.09 


35.94 97 


98 


91.49 


35.12 


91.34 


35.52 


191.18 


35.92 


91.02 


36,31 98 


99 


92.42 


35.48 


92.27 


35.88 


: 92.11 


36.28 


91.95 


36.69 99 


100 


93.36 


35.84 


93.20 


36.24 II 93.04 


36.65 


92.88 


37.06 


100 

o 


Dcp. 


Lat. 


Dep. 


Lat. I| Dep. 


Lat. 


Dep. 


J-at. 


69 Deg. 


681 Deg. 


1 

68^ Deg. 


68i Dog 



22 



116 



TRAVERSE TABLE. 



1 

I" 


22 


Dog. 


2Si Deg. 


22^ Deg. 


22? 


Deg. 


X 

~1 


Lat. 


Dep. 


Lat 


Dep. j 


Lat. 


Dep. 


Lat, 


Dep. 


6.93 


0.37 1 0.93 


0.38 


0.92 


0.38 


0.92 


0.39 


o 


1.85 


0.75' 1.85 


0.76 


1.85 


0.77 1 


1.84 


0.77 


2 


3 2.78 


1.121 2.73 


1.14 


2.77 


1.15 


2.77 


1.16 


3 


4 


3.71 


1.50 3.70 


1.51 


3.70 


1.53 


3.69 


•.55 4 1 


5 


4.64 


1.87 1 4.63 


1.89 


4.62 


1.91 j 


4.61 


i.93 


5 


6 


5.56 


2.25 


5.55 


2.27 i 5.54 


2.30 


5.53 


2.32 


6 


7 


6.49 


2.62 


6.48 


2.65 1 6.47 


2.68 


6. 40 


2.71 


7 


8 


7.42 


3.00 


7.40 


3.03 7.39 


3.06 7 38 


3.09 


8 


9 


8.34 


3.37 


8.33 


3.41' 8.31 


3.44 8.30 


3.48 9 1 


10 


9.27 


3.7c 


9.26 


3.79 9.24 


3.83 


9.22 


3.87 


10 
-ll 


11 


10.20 


4.12 


10.18 


4.17 10.16 


4.21 


10.14 


4.25 


12 1 11.13 


4.50 '11.11 


4.54! 11.09 


4.59 


11.07 


4.64 


12 


13 


12.05 


4.87 12.03 


4.92 12.01 


4.97 


11.99 


5.03 


13 


14 


12.98 


5.24 12.96 


5.30 12.93 


5.36 


12.91 


5.41 


14 


15 


13.91 


5.62 13.88 


5.08 : 13.86 


5.74! 


13.83 


5.80 15 


16 


14. S3 


5.99 14.81 


6.06 14.78 


6.12 


14.76 


6.19 j 16 


17 


15.76 


6.37 15.73 


6.44 15.71 


6.51 


15.68 


6.57 t 17 


18 


16.69 


6.74 16.66 


6.82 16.63 


6.89 


16.60 


6.96 18 


19 


17.62 


7.12 ! 17.59 


7.19 |i 17.55 


7.27 


17.52 


7.35 ! 19 


20 


18.54 


7.49 18.51 


7.57 j 


18.48 
19.40 


7.65 
8.04 


18.44 


7.73' 20 


21 


19.47 


7.87 1,19.44 


7.95! 


19.37 


8.12 i 21 


22 


20.40 


8.24! 20.36 


8.33 |! 20.33 


8.42 


20.29 


8.51 1 22 


23 


21.33 


8.62!' 21.29 


8.71 l; 21.25 


8.80 


21.21 


8.89 1 23 


24 


22.25 


8.99 22.21 


9.09 22.17 


9.18 :' 22.13 


9.23 1 24 


2.5 


23.18 


9.37 23.14 


9.47 I 23.10 


9.57 23.05 


9.67 1 25 


26 


24.11 


9.74 ,24.06 


9.84 24.02 


9.95 23.98 


10.05 ! 26 


27 


25.03 


10.11 124.99 


10.22 24.94 


10.33 24.90 


10.44: 27 


28 


25.96 


10.49 


25.92 


10.60 ; 25.87 


10.72, 25.82 


10.83 ' 23 


20 


26.89 


10.86 


26.84 


10.98 ! 26.79 


11.10 26.74 


11.21 1 29 


30 


27.82 


11.24: 


27.77 
23.69 


11.36 ; 27.72 
11.74 1 23.64 


11.48! 27.67 
11.86 28.59 


11.60 30 
11.99. 31 


31 


28.74 


11.61 


32 


29.67 


11.99 


29.62 


12.12 29.56 


12.25 29.51 


12.37! 32 


33 


30.60 


12.36 


30.54 


12.50 i 30.49 


12.63 30.43 


12.76 I 33 


34 


31.52 


12.74 


31.47 


12.87 1 31.41 


13.01 31.35 


13.15 


34 


35 


32.45 


13.11 


32.39 


13.25 1 32.34 


13.39 


32.28 


13.53 


2i, 


36 


33.33 


13.49 


33.32 


13.63 : 33.26 


13.73 


33.20 


13.92 


36 


37 


34.31 


13.86 


34.24 


14.01 1 34.18 


14.16 


34.12 


14.31 


37 


33 


35.23 


14.24 


35.17 


14.39 1 35.11 


14.54 


135.04 


14.70 


33 


39 


36.16 


14.61' 


36.10 


14.77 36.03 


14.92 


35.97 


15.08 


39 


40 


37.09 


14. 9S 
15.36 


37.02 
37.95 


15.15 
15.52 


36.96 


15.31 
15.69 


; 36.89 


15.47 


40 


41 i 33.01 


37.83 


[37.81 


15.86 


41 


42 


38.94 


15.73 


38.87 


15.90 33.80 


16.07 


33.73 


18.24 42 


43 


39.87 


16.11 


39.80 


16.23 : 39.73 


16.46 


39.65 


16.63 43 


4^1 


40.80 


16.48 


40.72 


16.66 40.65 


16.84 


'40.58 


17.02 


44 


45 


41.72 


16.86 


41.65 


17.04 , 41.57 


17.22 


.41.50 


17.40 


45 


46 


42.65 


17.23 


42.57 


17.42 ' 12.50 


17.60 


42.42 


17.79 


46 


47 


43.53 


17.61 


-13.50 


17.80 43.42 


17.99 


,43.34 


13.13 


47 


48 144.50 


17.93 


44.43 


18.18 : 44.35 


18.37 


1 44.27 


18.56 


•iS 


49 145.43 


18.36 


45.35 


18.55 : 45.27 


18.75 


145.19 


18.95 


49 


60 


46.36 


18.73 


46.28 


18.93 1 46.19 


19.13 
Lat. 


,46.11 


19.34 


50 

1 


Dep. 


Lat. 


Dep. 


Lat. Dep. 


Dep. 


Lat. 












Q 


68 1 


Deg. 


671 


Deg. 674 


Deg. 


67i 


Deg. 





TRAVERSE TABLE. 



117 





22 Deg. 


m Deg. 


22^ Deg. j 

1! 


22| Deg. 


§ 

o 

CO 

Ti 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


47.29 


19.10 


47.20 19.3li 


47.12 


19.52 


47.03 


19.72 


52 


48.21 


19.48 


48.13 1 19.69 i 


48.04 


19.90 


47.95 


20.11 


52 


53 49.14 


19.85 


49.05 20.07 


48,97 


20.28 


48.88 


20.50 


53 


54 50.07 


20.23 


49.98 20.45 


49.89 


20.66 


49.80 


20.88 


54 


55 


51.00 


20.60 


50.90 20.83 


50.81 


21.05 


50.72 


21.27 


r.5 


56 


51.92 


20.98 


51.83 


21.20 


51.74 


21.43 


51.64 


21.66 


56 


57 


52.85 


21.35 


52.76 


21.58 


52.66 


21.81 


52.57 


22.04 


57 


58 


53.78 


21.73 


53.68 


21.96 


53.59 


22.20 


.53.49 


22.43 


58 


59 


54.70 


22.10 


54.61 


22.34 


54.51 


22.58 


54.41 


22.82 


59 


60 
61 


55.63 


22.48 


55.53 


22.72 


55.43 
56.36 


22.96 


55.33 


23.20 


60 
61 


56.56 


22.85 


56.47 


23.10 


23.34 


56.25 


23.. 59 


62 


57.49 


23.23 


57.38 


23.48 


57.28 


23.73 


57.18 


23.98 


62 


6.J 


58.41 


23.60 


58.31 


23.85 


58.20 


24.11 


58.10 


24.36 


63 


64 


59.34 


23.97 


59.23 


24.23 


59.13 


24.49 


59.02 


24.75 


64 


65 


60.27 


24.35 


60.16 


24.61 


60.05 


24.87 


59.94 


25.14 


65 


66 


61.19 


24.72 


61.09 


24.99 


60.98 


25.26 


60.87 


25.52 


66 


67 


62.12 


25.10 


62,01 


25.37 


61.90 


25.64 


61.79 


25.91 


67 


68 


63.05 


25.47 


62.94 


25.75 


62.82 


26.02 


62.71 


26.30 


68 


69 


63.98 


25.85 


63.86 


26.13 


63.75 


26.41 


63.63 


26.68 


69 


70 
71 


64.90 


26.22 


64.79 


26.51 


64.67 


26.79 


64.55 


27.07 


70 

71 


65.83 


26.60 


65.71. 


26.88 


65.60 


27.17 


65.48 


27.46 


72 


66.76 


26.97 


66.64 


27.26 


66 52 


27.55 


66.40 


27.84 


72 


73 


67.68 


27.35 


67.56 


27.64 


67.44 


27.94 


67.32 


28.23 


73 


74 


68.61 


27.72 


68.49 


28.02 


68.37 


28.32 


68.24 


28.62 


74 


75 


69.54 


28.10 


69.42 


28.40 


69.29 


28.70 


69.17 


29.00 


75 


76 


70.47 


28.47 


70.34 


28.78 


70.21 


29.08 


70.09 


29.39 


76 


77 


71.39 


28.84 


71.27 


29.16 


71.14 


29.47 


71.01 


29.78 


77 


78 


72.32 


29.22 


72.19 


29.53 


72.06 


29.85 


71.93 


30.16 


78 


79 


73.25 


29.59 


73.12 


29.91 


72.99 


30.23 


72.85 


30.55 


79 


80 
81 


74.17 


29.97 


74.04 


30.29 


73.91 


30.61 


73.78 


30.94 


80 

81 


75.10 


30.34 


74.97 


30.67 


74.83 


31.00 


74.70 


31.32 


82 


76.03 


30.72 


75.89 


31.05 


75.76 


31.38 


75.62 


31.71 


82 


83 


76.96 


31.09 


76.82 


31.43 


76.68 


31.76 


76.54 


32.10 


83 


84 


77.88 


31.47 


77.75 


31.81 


77.61 


32.15 


77.46 


32.48 


84 


85 


78.81 


31.84 


78.67 


.32.19 


78.53 


32.53 


78.39 


32.87 


85 


86 


79.74 


32.22 


79.60 


32.56 


79.45 


32.91 


79.31 


33.26 


86 


87 


80.66 


32.59 


80.52 


32.94 


80.38 


33.29 


80.23 


33.64 


87 


88 


81.59 


32.97 


81.45 


33.32 


81.30 


33.68 


81.15 


34.03 


88 


89 


82.52 


33.34 


82.37 


33.70 


82.23 


34.06 


82.08 


34.42 


89 


90 
91 


83.45 


33.71 


83.30 


34.08 


83.15 


34.44 


83.00 


34.80 


90 
91 


84.37 


34.09 


84.22 


34.46 


84.07 


34.82 


83.92 


35.19 


9£ 85.30 


34.46 


85.15 


34.84 


85.00 


35.21 


84.84 


35.58 


92 


93 


86.23 


34.84 


86.08 


35.21 


85.92 


35.59 


85.76 


35.96 


93 


94 


1 87.16 


35.21 


87.00 


35.59 


86.84 


35.97 


86.69 


36.35 


94 


95 


;8S.08 


35.59 


87.93 135.97 


87.77 


36.35 


87.61 


36.74 


95 


96 


89.01 


35.96 


88.85 


36 35 


88.69 


33.74 


88.53 


37.12 


96 


97 


: 89.94 


36.34 


89.78 


36.73 


89.62 


37.12 


89.45 


37 51 


97 


9S 


90.86 


36.71 


90.70 


37.11 


90.54 


37.50 


90.38 


37.90 


98 


99 91.79 


37.09 


91.63 


37.49 


191.46 


37.89 


91.30 


38.28 


99 


100 


92.72 


37.46 


92.55 


37.86 


92.39 


38.27 


92.22 


38.67 


100 

1 

o 


y 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 

s 


! 68 Deg. 


67| Deg. 


&7^Deg. 


67i De^. 



118 



TRAVKRSE TABLE. 





23 Deg. 


23i Deg. 


23i 


Deg. 


231 Deg. 


CO 

p 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. Dep. 


i 0.92 


0.39 


0.92 


0.39 


0.92 


0.40 


0.92 0.40 


"■"l 


2 1.84 


0.78 


1.84 


0.79 


1.83 


0.80 


1.83 0.81 


2 


3 2.78 


1.17 


2.76 


1.18 


2.75 


1.20 


2.75 


1.21 


3 


4 S.68 


1.56 


3.68 


1.58 


3.67 


1.59 


3.66 


1.61 


4 


5 A. GO 


1.95 


4.59 


1.97 


4.59 


1.99 


4.58 


2.01 


5 


6 5.52 


2.34 


5.51 


2.37 


5.50 


2.39 


5.49 


2.42 


6 


7 6.44 


2 74 


6.43 


2.76 


6.42 


2.79 


6.41 


2.82 


7 


8 


7.36 


3.13 


7.35 


3.16 


7.34 


3.19 


7.32 


3.22 


8 


9 


8.28 


3.52 


8.27 


3.55 


8.25 


3.59 


8.24 


3.62 


9 


10 


9.20 


3.91 
4.30 


9.19 


3.95 


9.17 


3.99 


9.15 
10.07 


4.03 
4.43 


'0 
11 


'll 


10.13 


10.11 


4.34 


10.09 


4.39 


12 


11.05 


4.69 


11.03 


4.74 


11.00 


4.78 


10.98 


4.83 


12 


13 


11.97 


5.08 


11.94 


5.13 


11.92 


5.18 


11.90 


5.24 


13 


14 


12.89 


5.47 


12.86 


5.. 53 


12.84 


5.58 


12.81 


5.64 


14 


15 


13.81 


5.86 


13.78 


5.92 


13.76 


5.98 


13.73 


6.04 


15 


16 


14.73 


6.25 


14.70 


6.32 


14.67 


6.38 


14.64 


6.44 


16 


17 


15.65 


6.64 


15.62 


6.71 


15.59 


6.78 


15.56 


6.85 


17 


18 


J6.57 


7.03 


16.54 


7.11 


16.51 


7.18 


16.48 


7.25 


18 


19 


]7.49 


7.42 


17.46 


7.50 


17.42 


7.58 


17.39 


7.65 


19 


20 


18.41 


7.81 


18.38 


7.89 


18.34 
19.26 


7.97 


18.31 


8.05 


20 


21 


19.33 


8.21 


19,29 


8.29 


8.37 


19.22 


8.46 


21 


22 


20.25 


8.60 


20.21 


8.68 


20.18 


8.77 


20.14 


8.86 


22 


23 


21.17 


8.99 


21.13 


0.08 


21.09 


9.17 


21.05 


9.26 


23 


24 


22.09 


9.. 38 


22.05 


9.47 


22.01 


9.57 


21.97 


9.67 


24 


25 


23.01 


9.77 


22.97 


9.87 


22.93 


9.97 


22.88 


10.07 


25 


26 


23.93 


iO.iO 


23.89 


10.26 


23.84 


10.37 


23.80 


10.47 


26 


27 


24.85 


.0.55 


24.81 


10.66 


24.76 


10.77 


24.71 


10.87 


27 


28 


25.77 


.0.94 


25.73 


11.05 


25.68 


11.16 


25.63 


1.1.28 


28 


29 


26.69 


U.33 


26.64 


11.45 


26.69 


11.56 


26.54 


11.68 


29 


30 
31 


27.62 


11.72 


27.56 


11.84 


27.51 


11.96 


27.46 


12.08 


30 


28.54 


12.11 


28.48 


12.24 


28.43 


12.36 


28.37 


12.49 


31 


32 


29.46 


12.50 


29.40 


12.63 


29.35 


12.76 


29.29 


12.89 


32 


33 


30.38 


12.89 


30.32 


13.03 


30.26 


13.16 


30.21 


13.29 


33 


34 


31.30 


13.28 


31.24 


13.42 


31.18 


13.56 


31.12 


13.69 


34 


35 


32.22 


13.68 


32.16 


13.82 


32.10 


13.96 


32.04 


14.10 


35 


36 


33.14 


14.07 


33.08 


14.21 


33.01 


14.35 


32.95 


14.50 


36 


37 


34.06 


14.46 


34.00 


14.61 


,33.93 


14.75 


33.87 


14.90 


37 


38 i 34.98 


14.85 


34.91 


15.00 


34.85 


15.15 


34.78 


15.30 


38 


39 


35.90 


15.24 


35.83 


15.39 


35.77 


15.55 


35.70 


15.71 


39 


40 


36.82 


15.63 


36.75 


15.79 


36.68 


15.95 


36.61 


16.1! 


40 


41 


37.74 


16.02 


37.67 


16.18 


37.60' 


16.35 


37.53 


16.51 


\l 


42 


38.66 


16.41 


38.59 


16.58 


38.. 52 


16.75 


38.44 


16.92 


12 


43 


39.58 


16.80 


39.51 


16.97 


39.43 


17.15 


39.36 i 17.32 


43 


44 


40.50 


! 17.19 


40.43 


17.37 


40.35 


17.54 


40.27 


17.72 


44 


45 ! 41.42 


17.58 


41.35 


17.76 


41.27 


17.94 


41.19 


18.12 


45 


46 42.34 


17.97 


42.26 


18.16 


42.18 


18.34 


42.10 


18.53 


46 


47 43.26 


18.36 


43.18 


18.55 


43.10 


18.74 


43.02 


18.93 


47 


48 44.18 


1 18.76 


44.10 


18.95 


44.02 


19.14 


43.93 


19.33 


48 


19 45.10 


19.15 


45.02 


19.. 34 


44.94 


19.54 


44.85 


19.73 


49 


50 46.03 


1 19.54 


45.94 


19.74 


45.85 


19.94 


145.77 


20.14 


50 

§ 


i 


1 Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


C 


1 67 


Deg 


661 


Deg. 


66i 


Deg. 


66i 


Deg. 



TRAVERSE TA.BLE. ' 



119 



p 

n 
o 


23Deg. 


23i Deg. 


23i Deg. 


23| Deg. 


o 

P 

3 

51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat 1 Dep. 


46.95 


19.93 


46.86 


20.13 


46.77 


20.34 


46.68 20.54 


52 


47 87 


20.32 


47.78 


20 . 53 


47.69 


20 . 73 


47.60 120.94 


52 


53 


48.79 


20.71 


48.70 


20.92 


48.60 


21.13 


48.51 21.35 


53 


54 


49.71 


21.10 


49.61 


21.32 


49.52 


21.53 


49.43 121.75 


54 


55 


50,63 


21.49 


50.53 


21.71 


50.44 


21.93 


50.34 122.15 


55 


56 


51.55 


21.88 


51.45 


22.11 


51.36 


22.33 


51.26 22.55 


56 


57 


52.47 


22.27 


52.37 


22.50 


52.27 


22.73 


52.17 22.96 57 


5S 


53.39 


22.66 


53.29 


22.90 


53.19 


23.13 


53.09! 23.36 58 


59 


.54.31 


23.05 


54.21 


23.29 


54.11 


23.53 


54 00 


123.76 , 591 


60 
61 


55.23 


23.44 


55.13 


23.63 


55.02 


23.92 


54.92 


24.16 


60 


56. 15 


23.83 


56.05 


24.03 


55.94 


24.32 


55.83 


24.57 


Tl 


62 


57.07 


24.23 


56.97 


24 47 


56.85 


24.72 


56.75 


24.97 


62 


63 


57.99 


24.62 


57. 8S 


24.87 


57.77 


25.12 


57.66 


25.37 


63 


64 


53.91 


25.01 


58.80 


25.26 


58.69 


25.52 


58.58 


25.78 


64 


65 


59.83 


25.40 


59.72 


25.66 


59.61 


25.92 


59.50 


26.18 


65 


66 


60.75 


25.79 


60.64 


26.05 


60.53 


26.32 


60.41 


26.58 


66 


67 


61.67 


26.18 


61.56 


26 . 45 


61.44 


20.72 


61.33 


26.93 


67 


68 


62.59 


28.57 


62.48 


26.34 


62.36 


27.11 


62.24 


27.39 


68 


69 


63.51 


26.96 


63.40 


27.24 


63.23 


27.51 


63.16 


27.79 


69 


70 
71 


64.44 
65.. 36 


27.35 


64.32 
65.23 


27.63 


64.19 


27.91 


64.07 


28.19 


70 
71 


27.74 


23.03 


65.11 


23.31 


64.99 


23.59 


72 


66.28 


23.13 


66.15 


23.42 


66.03 


23.71 


65.90 


29.00 


72 


73 


67.20 


28.52 


67.07 


23.82 


66.95 


29.11 


66.82 


29.40 


73 


74 


63.12 


23.91 


67.99 


29.21 


67.86 


29.51 1 


67.73 


29.80 


74 


75 


69.04 


29.30 


68.91 


29.61 


63.78 


29.91 


68.65 


30.21 


75 


76 


69.96 


29.70 


69.83 


30.00; 


69.70 


30.30 


69.. 56 


30.61 


76 


77 


70.88 


30.09 


70.75 


30.40 


70.61 


30.70 


70.43 


31.01 


77 


78 


71.80 


30.48 


?l-.67 


30.79 


71.53 


31.10 


71.39 


31.41 i 73 


79 


72.72 


30.87 


72.53 


31.18 


72.45 


31.50 


72.31 


31.82 1 79 


80 
81 


73.64 


31.26 


73.50 


31.53 


73.36 


31.90 


73.22 


32.22 1 80 


74.56 


31.65 


74.42 


31.97 


74.28 


35i.30 


74.14 


32.62 81 


82 


75.43 


32.04 


75.34 


,32.37 


75.20 


32.70 


75.06 


33.03 82 


83 


70.40 


32.43 


76.26 


32.76 


76.12 


33.10 


75.97 


33.43 83 


84 


77.32 


32.82 


77.18 


33.16 


77.03 


33.49 


76.89 


33.83 84 


85 


78.24 


33.21 


78.10 


33.55 


77.95 


.33.89 


77.80 


34.23 1 85 


86 


79.16 


33.60 


79.02 


33.95 


78.-87 1 34.29 


78.72 


34.64! 86 


87 


80.08 


33.99 


79.93 


34.34 


79.78 1 34.69 


79.63 


35.04 


87 


88 


81.00 


34.33 


80.85 


34.74 


80.70 i 35.09 


80.55 


35.44 


88 


89 


81.92 


34.78 


81.77 


35.13! 


81.62' 35.49 


81.46 i 35.84 


89 


90 
91 


82.85 


35.17 


82.69 


35.53 i 


82.54; 35.89 


82.33 


36.25 


90 
91 


83.77] 35.56 


83.61 


35.92 


83.45: 36.29 1 


83.29 


36.65 


92 


84.69! 35.95 


84.53 


36.32 


84.37 136.63 1 


84.21 


37.05 92 


93 


85.61 : 36.34 


85.45 


36.71 j 


85.29 37.08 1 


85.12 


37.46 93 


94 


86.53 36.73 


86.37 


37.11 1 


86.20 37.48; 


86.04 


37.86 ' 94 


95 


87.45 37.12 


87.29 


37.50 i 


87.12 37.83! 


86.95 


38.26 


95 


96 


88.37 37.51 


83.20 


37.90] 


88.04 33.28 i 


87.87 


,38.66 


^6 


97 89.29,37.90 


89.12 


3S.29i 


83.95 38.63 


88.79 


39.07 


97 


98 90.21 39.29 


90.04 


33.68^ 


89.87 39.03 


89.70 


39.47 


98 


99 


91.13 33.63 1 


90.96 


39.08! 


90.79 39.48 


90.62 


39.87 


99 


^00 


92.05 
Dep. 


39.07 


91.83 


39.47 1 


91.71 139.871 


91.53 


40.27 


100 


Lat. 


Dep. 


Lat. 


Dep 1 Lat. 


Dep 


Lat. 


a 
3 


67 Deg. 

i 


661 Deg. 


661 Deg. 


66,^ Deg. ; 



120 



TRAVERSE TABLE. 



o 

? 


24 Deg. 


24i Deg. 


24^ 


Deg. 


1 

24| Deg. 


1 

C 
5' 
§" 

a 

a 


Lat. 


Dep. 


Lat. 


Dep. 


Lai. 


Dep. 


Lat. 


Dep. 


^ 


0.91 


: 0.41 


0.91 


0.41 


0.91 


0.41 


0.91 


0.42 


'~l 


2 


1.83 


0.81 


1.82 


0.82 


1.82 


0.83 


1.82 


0.84 


2 


3 


2.74 


: 1.22 


2.74 


1.23 


2.73 


1.24 


2 72 


1.26 


3 


4 


3.65 


. 1.63 


3.65 


1.64 


3.64 


1.66 


3.63 


1.67 


4 


5 


4.57 


2.03 


4.56 


2.05 


4.55 


2.07 


4.54 


2.09 


5 


6 


5.48 


2.44 


5.47 


2.46 


5.46 


2.49 


6.45 


2.51 


6 


7 


6.39 i 2.85 


6. 38 


2.87 


6.37 


2.90 


6.36 


2.93 


7 


8 


7.31 1 3.25 


7.29 


3.29 


7.28 


3.32 


7.27 


3.35 


8 


9 


8.22' 3.66 


8.21 


3.70 


8.19 


3.73 


8.17 


3.77 


9 


10 


9.141 4.07 


9.12 


4.11 


9.10 


4.15 


9.08 


4.19 


lO 


11 


10.05; 4.47 


10.03 


4.52 


10.01 


4.56 


9.99 


4.61 


11 


12 


10.96 i 4.88 


10.94 


4.93 


10.92 


4.98 


10.90 


5.02 


12 


13 


11.88 1 5.29 


11.85 


5.34 


11.83 


5.39 


11.81 


5.44 


13 


14 


12.79 1 5.69 


12.76 


5.75 


12.74 


5.81 


12.71 


5.86 


14 


15 


13.70 1 6.10 


13.68 


6.16 


i 13.65 


6.22 


13.62 


6.28 


15 


16 


14.62' 6.51 


14.59 


6.57 


14.56 


6.64 


14.53 


6.70 


16 


17 


15.53 i 6.92 


15.50 


6.98 


15.47 


7.05 


15.44 


7.12 


17 


18 


16.44 7.32 


16.41 


7.39 


16.38 


7.46 


16.35 


7.54 


18 


19 


J7.36 7.73 


17.32 


7.80 


17.29 


7.88 


17.25 


7.95 


19 


20 
21 


18.27 8.13 
19.18 , 8.54 


18.24 


8.21 


18.20 
19.11 


8.29 


18.16 
19.07 


8.37 


20 

21 


19.15 


8.63 


8.71 


8.79 


"2 


20.10 1 8.95. 


20.06 


9.04 


20.02 


9.12 


' 19.98 


9.21 


22 


23 


21.01 1 9.35 , 


20.97 


9.45 


20.93 


9.54 


20.89 


9.03 


23 


24 


21.93 1 9.76 ' 


,21.88 


9.86 


21.84 


9.95 


21.80 


10.05 


24 


25 


22.84! 10.17 


22.79 


10.27 


22.75 


10.37 


22.70 


10.47 


25 


26 


23.75 : 10.58 


23.71 


10.68 


23.66 


10.78 


23.61 


10.89 


26 


27 


24.67 ' 10.98 


24.62 


11.09, 


24.57 


11.20; 


24.52 


11.30 


27 


28 


25. .58 i 11.39 ' 


25 . 53 


11.50 i 


25.48 


11.61 


25.43 


11.72 


28 


29 


26.49 1 11.80 


26.4-1 


11.91 ' 


26.39 


12.03! 


26.34 


12.14 


29 


30 
31 


27.41 • 12.20 1 
28.32 12.61 1 


27.35 
28.26 


12.32 


27.30 

28.21 


12.44' 
12.86 ■■ 


27.24 


12.56 


30 

31 


12.73! 


28.15 


12.93 


32 


29.23 13.02 • 


29.18 


13.14i 


29.12 


13.27: 


29.06 


13.40 


32 


33 


30.15 13.42' 


30.09 13.55: 


30.03 


13.63 : 


29.97 


13.82 


33 


34 


31.06 13.83 


31. 00113. 96; 


30.94 


14.10 ! 


30.88 


14.23 


34 


35 


31.97 14.24 


31.91 


14. 3S 


31.85 


14.51 


31.78 


14.65 


35 


36 


32.89 ■ 14.64 


32.82 


14.79: 


32.76 


14.93 


32.69 


15.07 


36 


37, 


33.80 15.05 


33.74 


15.20; 


33.67 


15.34; 


33.60 


15.49 


37 


38,' 


34.71 15.4fi ' 


34.65 


15.61 i 


34.58 


15.76 i 


34.51 


15.91 


38 


39 1 


35.63 


15.86 ; 


35.56 ! 16.02 


.35.49 


I6.17i 


.35.42; 


16.33 


39 


40 ; 


36.54 


16.27 i 


36.47 i 16.43 


36.40 


16.59 ! 


36.33 ' 


16.75 


40 


411 


37.46 


16.68 


37.38; 16.84! 


37.31 1 


17.00 i 


37.23 


17.16 


41 


42 


38.37 


17.03 


33.29 ; 17.25 I 


38.22; 


17.42 


38.14 


17.58 


42 


43! 


39.28 


17.49 


39.21 17.60 i 


39.13 


17.83; 


39.05 1 


13.00 


43 


441 


40.20 


17.90 


40.12 ! 13.071 


40.04; 


18.25 1 


39.96 : 


18.42 


44 


45 


41.11 


18 30 ; 


41.03 ; 18.48 i 


40.95 


18.66 


40.87! 


18.84 


45 


46 i 


42.02 '18.71 


41.94 


18.89 


41.86 ! 


19.03 


41.77 1 


19.26 


46 


47 ' 


42.94 19.12 


42.85 


19.30 


42.77 


19.49 


42.63 


19. 6S 


47 


48 -43.85 19.52 


43 . 70 


19.71 


43.63 ' 


19.91 


43.59 ' 


20.10 


48 


49 '44.76 19.93 


44.68 


20.131 


44.59 ' 


20 . 32 


44.50 i 


20.51 


49 


50; 

1 ! 


45.68 20.34 


45.59 


20.54 


45.50 , 


20.73 


45.41 1 
Dep. 


20.93 
Lat. 


_50 

6 

1 

Q 


Dep. i Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


66 r 


)eg. 


651 Deg. 1 


651 1 


D'^.g. 


65J Deg. 



"A. 



TKAVEUSE TABLE. 



121 



5 
P 
51 


24 Deg. 


24i Deg. 


24i Deg. 


241 Dej. 


1 

? 
51 


Lat. 

46.59 


Dep. 


r 
Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


20.74 


46.50 


20.95 


46.41 


21.15 


46.32 


21.35 


52 


47.50 


21.15 


47.41 


21.36 


47.32 


21.56 


47.22 21.77 


52 


53 


48.42 


21.56 


48.32 


21.77 


48.23 


21.98 


48.13 


22.19 


53 


54 


49.33 


21.96 


49.24 


22.18 


49. H 


22.39 


49.04 


22.61 


54 


55 


50.24 


22.37 


50.15 


22.59 


50.05 


22.81 


49.95 


23.03 


55 


56 


51.16 ! 22.78 


51.06 


23.00 


50.96 


23.22 


50.86 


23.44 


56 


57 


52.07 123.18 


51.97 


23.41 


151.87 123.64 


51.76 


23.86 


57 


58 


52.99 23.59 


52.88 


23.82 


52.78 


24.05 


52.67 


24.28 


58 


59 


53.90 


24.00 


53.79 


24.23 


i 53.69 


24.47 


53.58 


24.70 


59 


60 
"61 


54.81 


24.40 


54.71 


24.64 


j 54.60 


24.88 


54.49 


25.12 


60 
61 


55.73 


24.81 


55.62 


25.05 


55.51 


25.30 


55.40 


25.54 


62 


56.64 


25.22 


56.53 


25.46 


56.42 


25.71 


56.30 


25.96 


62 


63 


57.55 


25.62 


57.44 


25.88 


57.33 


26.13 


57.21 


26.38 


63 


64 


58.47 


26,03 


58.35 


26.29 


58.24 


26.54 


58.12 


26.79 


64 


65 


59.38 


26.44 


59.26 


26.70 


59.15 


26.96 


59.03 


27.21 


65 


66 


60.29 


26.84 


60.18 


27.11 


60.06 


27.37 


59.94 


27.63 


66 


67 


61.21 


27.25 


61.09 


27.52 


60.97 


27.78 


60.85 


28.05 


67 


68 


62.12 


27.66 


62.00 


27.93 


61.88 


28.20 


61.75 


28.47 


68 


69 


63.03 


28.06 


62.91 


28.34 


62.79 


28.61 


62.66 


28.89 


69 


70 
"7l 


63.95 


28.47 


63. &2 


28.75 


63.70 


29.03 


63.57 


29.31 
29.72 


70 
71 


64.86 


28.88 


64.74 


29.16 


64.61 


29.44 


04.48 


72 


65.78 


29.28 


65.65 


29.57 


65.52 


29.86 


65.39 


30.14 


72 


73 


66.69 


29.69 


66.56 


29.98 


66.43 


30.27 


66.29 


30.56 


73 


74 


67.60 


30.10 


67.47 


30.39 


67.34 


30.69 


67.20 


30.98 


74 


75 


68.. 52 


30.51 


68.38 


30.80 


68.25 


31.10 


68.11 


31.40 


75 


76 


69.43 


30.91 


69.29 


31.21 


69.16 


31.52 


169.02 


31.82 


76 


77 


70.34 


31.32 


70.21 


31.63 


70.07 


31.93 


169.93 


32.24 


77 


78 


71.26 


31.73 


71.12 


32.04 


70.98 


32.35 


'70.84 


32.66 


78 


79 


72.17 


32.13 


72.03 


32.45 


71.89 


32.76 


i 71.74 


33.07 


79 


80 
81 


73.03 


32.54 


72.94 


32.86 


72.80 


33.18 


i 72.65 


33.49 


80 
81 


74.00 32.95 


73.85 


33.27 


73.71 


33.59 


i 73.56 


33.91 


82 


74.91 33.35 


74.76 


33.68 


74.62 


34.00 


; 74.47 


34.33 


82 


83 


75.82 33.76 


75.68 


34.09 


75.53 


34.42 


75.38 


34.75 


83 


84 


76.74 


34.17 


76.59 


34.50 


76.44 


34.83 


; 76.28 


35.17 


84 


85 


77.65 


34.57 


77.50 


34.91 


77.35 


35.25 


77.19 


35.59 


85 


86 


78.56 


34.98 


78.41 


35.32 


78 26 


35.66 


1 78.10 


36.00 


86 


87 


79.43 


35.39 


79.32 


35.73 


79.17 


36.08 


79.01 


36.42 


87 


88 


80.39 


35.79 


80.24 


36.14 


80.08 


36.49 


1 79.92 


36.84 


88 


89 


81.31 36.20 


81.15 


36.55 


80,99 


36.91 


i 80.82 1 37 26 


39 


90 
"91 


82.22 '36.61 


82.06 


36.96 


81.90 

82.81 


37.32 

37.74 


: 81.73 


37.68 
33.10 


90 
91 


83.13 37.01 


82.97 


37.. 38 


[82.64 


92 


84.05 


37.42 


83.88 


37.79 


83.72 


38.15 


83.55 


38.52 


92 


93 


84.96 


37.83 


84.79 


38.20 


84.63 


38.57 


84.46 


33.94 


93 


94 


85 87 


3S.2? 


85.71 


38.61 


85.54 


38.98 


85.37 


39.35 


94 


95 


86 79 


38.6/i 


86.62 


39.02 


86.45 


39.40 


86.27 


39 77 


95 


96 


87.70 


39.05' 


87.53 


39.43 


87.36 


39.81 


87.18 


40.19 


96 


97 


68.61 


3&.45 


38.44 


39.84 


88.27 


40.23 


88.09 


40.61 


97 


98 


39.5:3 ! 39.0-3 


89.35 


40.25 


89.18 


40.64 


89.00 


41.03 


98 


99 


•^0.44 


40.^7 


90.26 


40.66 


90.09 


41.05 


89.91 


41.45 


99 


''7 

3 


•Jl.SO 
Dep. 


4ti).L7 
L?t. 


91.18 
Dop. 


41.07 


91.00 


41.47 


90.81 


41.87 


lOO 

6 

c 

Q 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


66 E 


><n. 


65| 


Deg. 


65J Deg. 


651 Deg. 



122 



TRAVERSE TABLE. 



1 

? 


25 Deg. 


1 

25i Deg, 


25iDeg 


25} Deg. 


5 

.i. 


Lat. ^ Dep. 
0.91 ! 0.42 


Lat. 


Dep. 


Lat. 


Dep. 


Le.t. 


Dep. 


0.90 


0.43 


0.90 


0.43 


0.90 


0.43 


2 


1.81 


0.85 


1.81 


0.85 


1.81 


0.86 


1.80 


0.87 


2 


3 


2.72 


1.27 


2.71 


1.28 


2.71 


1.29 


2.70 


1.30 


3 


4 


3.63 


1.69 


3.62 


1.7i 


3.61 


1.72 


3.60 


1.74 


4 


6 


4.53 


2.11 


4.52 


2.13 


4.51 


2.15 


4.50 


2.17 


5 


6 


5.44; 2.54 


5.43 


2.56 


6.42 


2.58 


5.40 


2.61 


6 


7 


6.34 i 2.96 


G.,33 


2.99 


6.32 


3.01 


6.30 


3.04 


7 


8 


7.25. 3.38 


7.24 


3.41 


7.22 


3.44 


7.21 


3.48 


8 


9 


8.16 


3.80 


8.14 


3.84 


8.12 


3.87 


8.11 


3. -91 


9 


10 


9.06 


4.23 


9.04 


4.27 


9.03 


4.31 


9.01 


4.34 


10 


if 


9.97 


4.65 


9.95 


4.69 


9.93 


4.74 


9.61 


4.78 


11 


12 


10.88 


5.07 


10.85 


5.12 


10.83 


5.17 


10.81 


5.21 


12 


13 , 11.78 


5.49 


11.76 


5.55 


11.73 


5.60 


11.71 


5.65 


13 


14 12. bO 


5.92 


12.66 


5.97 


12.64 


6.03 


12.61 


6.08 


14 


15 


13.59 


6.34 


13.57 


6.40 


13.54 


6.46 


13.51 


6.. 52 


15 


16 


14.50 


0.76 


14.47 


6.83 


14.44 


6.89 


14.41 


6.95 


16 


17 


15.41 


7.18 


15.38 


7.25 


15.34 


7.32 


15.31 


7.39 


17 


IS 


16.31 


7.61 1 


16.28 


7.68 


16.25 


7.75 


16.21 


7.82 


18 


19 


17.22 


8.03 1 


17.18 


8.10 


17.15 


8.18 


17.11 


8.25 


19 


20 
21 


18.13 
19.03 


8.45 1 


18.09 


8.53 


18.05 


8.61 


18.01 


8.69 
9.12 


20 
21 


8.871 


18.99 


8.96 


18.95 


9.04 


18.91 


22 


19.94 


9.30 


19.90 


9.38 


19.86 


9.47 


19.82 


9.56 


22 


23 


20.85 


- 9.72i 


20.80 


9.81 


20.76 


9.90 


20.72 


9.99 


23 


24 


21.75 


10.14 


21.71 


10.24 


21.66 


10.33 


21.62 


10. t3 


24 


25 


22.66 


10.57 


22.61 


10.66 


22.56 


10.76 1 


22.52 


10.86 


25 


2G 


23.56 


10.99 


23.52 


11.09 


23.47 


11.19 


23.42 


11.30 


26 


27 


24.47 


11.41 


24.42 


11.52 


24.37 


11.62 


24.32 


11.73 


27 


28 


25.38 


11,83 


25.32 


11.94 


25.27 


12.05 


25.22 


12.16 


28 


29 


26.28 


12.26 


26.23 


12.37 


26.17 


12.48 


26.12 


12.60 


29 


30 


27.19 


12.68 


27.13 


12.80 


27.08 


12.92 


27.02 


13.03 


30 


31 


28.10 


13.10 


28.04 


13.22 


27.98 


13.35 


27.92 


13.47 


31 


32 


29.00 


13.52 


28.94 


13.65 


28.88 


13.78 


28.82 


13.90 


32 


33 


29.91 


13.95 


29.85 


14.08 


29.79 


14.21 


29.72 


14.34 


33 


34 


30.81 


14.37 


30.75 


14.50 


30.69 


14.64 


30.62 


14.77 


34 


35 


31.72 


14.79 


31.66 


14.93 


31.59 


15.07 


31.52 


15.21 


35 


3G 


32.63 


15.21 


32.56 


15.36 


32.49 


15.50 


32.43 


15.64 


36 


37 


33.53 


15.64 


33.46 


15.78 


33.40 


15.93 


33.33 


18.07 


37 


38 


34.44 


16.06 


34.37 


16.21 


34.30 


16.36 


34.23 


16.51 


38 


39 


35.35 


16.48 


35.27 


16.64 


35.20 


16.79 


35.13 


16.94 


39 


40 
41 


36.25 


16.90 


36.18 


17.06 


36.10 


17.22 


36.03 


17.38 


40 
41 


37.16 


17.33 


37.08 


17.49 


37.01 


17.65 1 


36.93 


17.81 


42 


38.06 


17.75 


37.99 


17.92 


37.91 


18.08] 


37.83 


18.25 


42 


43 


38.97 


18.17 


38.89 


18.34 


38.81 


18.51 


38.73 


18.68 


43 


44 


39.88 


18.60 


39.80 


18.77 


39.71 


18.94 1139.63 


19.12 


44 


45 


40.78 


19.02 


40.70 


19.20 


40.62 


19.37 


40.53 


19.55 


45 


46 41.69 


19.44 


41.60 


19.62 


41.52 


19.80 


41.43 


19.98 


46 


47 42,60 


19.86 


42.51 


20.05 


42.42 


20.23 


42.33 


20.42 1 47 


48 43.50 


20.29 


43.41 


20.48 


43.32 


20.66 


43.23 


20.8.'5 1 -IS 


49 44.41 


20.71 


44.32 


20.90 


44.23 


21.10 


44.13 


21.29 ' 49 


50 


45.. 32 


21.13 


45.22 


21.33 


45.13 


21.53 


45.03 


21.72 


50 


.2 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1' 

1 


65 Deg. 


64| Deg. 


64i Dog. 


644 


Deg. 



TRAVERSE TABLE. 



123 



DC 


25 De^. 1 

1 


25+ Deg. 


25i Deg. 


25| Deg. 


1 

3 
P 

51 


Lat. 


Dep. 


Lat. 1 Dep. 
46.13 : 21.75 


|Lat. 


Dep. 


Lat. 


Dep. 


4^3722" 


21.55 


146.03 


21.96 


45.94 


22.16 


52 


47.13 21.93' 


47.03 22.18 


46.93 


22.39 


46.84! 22.59 


52 


53 


4S.03 {22.40 


47.94 22.61 


147.84' 22.82 


47.74 : 23.03 


53 


5t 


48.94: 22.82' 


48.84, 23.03 


|48.7i 


23.25 


48.64; 23.46 


54 


55 


49.85 123.24 


49.74 23.46 


I 49 . 64 


23.68 


49.54 23.89 


55 


5e 


50.75 23.67 


50.65 


23.89 


50.. 54 


24.11 ! 


50.44 1 24.33 


56 


57 


51 66 


24.09 


51.55 


24.31 


,51.45 


24.54 1 


51.34 1 24.76 


57 


5S 


52.57 


24.51 ■ 


52.46 


24.74 


i .52.35 


24.97 


52.24 i 25.20 


58 


59 


.53 47 


24.93 


53,36 


25.17 


'53.25 


25.40 


.53.14 25.63 


59 


60 


54 38 


25.36 


54.27 


25.59 


154.16 


25.83 


54.04 126.07 


60 


61 


55.23 


25.78 


55.17 


26.02 


55.06 


26.26! 


.54.94 1 26.50 


~61 


G2 


56.19 


26.20! 


.56.08 


26.45 


55.96 


2^.PJI 


55.84' 2P.9i 


62 


63 


57.10 


26 62 ' 


56.98 


26.87 


56.86 ^^7.12: 


06.74 


L7 37 


63 


64 


58.00 


27.05 


57.89 


27.30 


,57.77 27.55 • 


57.64 


27.80 


64 


65 


.58.91 


27.47 


58.79 


27.73 


58.67 27.98' 


58.55 


28.24 


65 


66 


59.82 


27.89 


59.69 


28.15 


59.57 23.41 i 


59.45 


28.67 


66 


67 


60.72 


28.32 


60.60 


28.58 


60.47 28.84' 


60.35 


29.11 


67 


68 


61.63 


28.74 


61.50 


29.01 


61.33 29.27 i 


61.25 


29 . 54 


68 


69 


62.54 


29.16; 


62.41 


29.43 


62.23 29.71 ] 


62.15 


29.98 


69 


70 
71 


63.44 


29.58 


63.31 


29.86 


63.18| 30.14! 


63.05! 30.41 


70 
71 


64.35 


30,01 


64.22 j 30.29 


64.03, 30.57! 


63.95 


30.85 


72 


65.25 1 30.43 


65.12 30.71 


64.99. 31.00 : 


64.85 


31.28 


72 


73 


66.18 [30.85 


66.03 I 31.14 


65.89! 31.43 1 


65 . 75 


31.71 


73 


74 


67.07 31.27 1 


66.93 j 31. .57 


66.79 31.86! 


66.65 


32.15 


74 


75 


67.97 ! 31.70 ; 


67.83 31.99 


67.69 32.29 


67.55 


32.58 


75 


76 


68.88 132.12 


68.74! 32.42 


68.60 32.72 j 


68.45 


33.02 


76 


77 


69.79 32.54 


69.64' 32.85 


69.50! 33.15 ! 


69.35 


33.45 


77 


78 


70.69 3*2.96 


70.55' 33.27 


70.40! 33.58 1 


70.25 


33.89 


78 


79 


71.60 33.39 


71.45 33.70 


71.30; 34.01 


71.16 34.32 


79 


80 
"8l 


72.50 '33.81 


72.36 34.13 


72.21 , 34.44 
73.11 i 34.8/ ! 


72.06 34.76 
72.96 1 35.19 


80 
81 


73.41 34.23 


73.26 , 34.55 


82 


74.32 ! 34.65 


74.17! 34.98 


74.01 j 35.30 


73.86 ! 35.62 


82 


83 


75.22 1 35.08 


75.07! 35.41 


74.91 1 35.73 


74.76 i 38.06 


83 


84 


76.13 135.50 


75.97; 35.83 


75.82: 36.16 


75.66 i 36.49 


84 


85 


77.04 135.92 


76.83 36.26 


76.72 36.59 


76.56 36.93 


85 


86 


77.94 iC6. 35 


77.78 36.68 


77.62 1 37.02 


77.46 ! 37. a6 


86 


87 


78.85 : 36.77' 


73.69 ' 37.11 


78.52; 37.45 


78.36! 37.80 


87 


88 


79.76 : 37.19 


79.59 37.54 


79.43! 37.88 


79.^26 ! 38.23 


88 


80 


80.66 ,37.61 


80.50 37.96 


80.33 1 38.32 


80.16 1 38.67 


89 


90 
91 


81.57 1 33.04 
82.47-38.46 


81.40 
82.31 


38.39 


81.23! 38.75 


81.06 I 39.10 
81.96 \ 39.53 


90 
91 


38.82 


82.14; 39.18 


92 


83.38 ,38.88 


83.21 : 39.24 


83.04; 39.61 


82.86 39.97 


92 


93 


84.29 139.30 


84.11 1 39.67 


83.94 40.04 


83.76 1 40.40 


93 


94 


85.19 1 39.73 


85.02 1 40.10 


84.84-40.47 


, 84.67 1 40.84 


94 


95 


86.10 40.15 


85.92 1 40.52 


85.75 40.90 


85 57 41.27 


95 


96 


87.01 140.57 


86.83 140.95 86.65 41.33 


86 47: 41.71 


96 


97 


87.91 i 40.99 


87.73 i 41.38 87.55 41.76 


87.37! 42.14 


97 


9S 


88.82 141.42 


88.64 141.80 88.45 42.19 


188.27! 42.58 


98 


99 


89.72 141.84 


189. .54 42.23 89.36 42.62 


.89.17 43.01 


09 


lOO 

d 
ri 

Li 


90.63 142.26 


190.45 142.66 


90.26 43.05 


90.07 j 4.^ 4-1 


1(^0 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. Lat. 


Dep. 1 Lat. 




65 


Deg. 


64| Deg. 

i 


! 

64i Deg. 


1 

; 64i Dej. 





124 



TRAVERSE TABLE. 



O ' 26 Deg. 


1 
264 Deg, ; 


1 
26^ Deg. 1 


26| Deg. 


c 


g! 








1 




en 


5 


I, at. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
0.89 


Dep. j 
0.45 


a 
P 
1 


~r 


0,90 


0.44 


0.90 


0.44 1 


0.89 


0.45 


2 1.801 


0.88 


1.79 


0.88 1 


1.79 


0.89 


1.79 


O.GO 


2 


3 


2.70 


1.32 


2.69 


1.33 


2.68 


1.34 


2.68 


1.35 


3 


4 


3.60 


1.75 


3.59 


1.77 1 


3.58 


1.78 


3.57 


1.80 '■ 


1 


5 


4.4a 


2.19 


4.48 


2.21 


4.47 


2.23 


4.46 


2.25 


5 


6 


5.39 


2.63 


5.38 


2.65 


5.37 


2.68 


5.ri6 


2.70 


6 


7 6.29 


3.07 


6.28 


3.10 


6.26 


3.12 


6.25 


3.15 


7 


8; 7.19 


3.51 


\.17 


3.54 


7.16 


3.57 


7.14 


3.60 


8 


9 8.09 


3.95 


8.07 


3.98! 


8.05 


4.02 


8.04 


4.05 


9 


10 


8.99 
9.89 


4.3S 

4.82 


8.97 


4.42 : 


8.95 


4.46 


8.93 


4.50 


10 
11 


9.87 


4.87 


9.84 


4.91 


9.82 


4.95 


12 


10.79 


5.26 


10.76 


5.31 


10.74 


5.35 


10.72 


5.40 


12 


13 


11. 6S 


5.70 


11.66 


5.75 


11.63 


5.80 


11.61 


5.85 


13 


14 


12.58 


6.14 


12.56 


6.19 


12.53 


6.25 


12.50 


6.30 


14 


15 


13.48 


6.58 


13.45 


6.63 


13.42 


6.09 


13.39 


6.75 


15 


16 


14.38 


7.01 


14.35 


7.08 


14.32 


7.14 


14.29 


7.20 


16 


17 


15.28 


7.45 


15.25 


7.52 


15.21 


7.59 


15.18 


7.65 


17 


18 


16.18 


7.89 


16.14 


7.96 


16.11 


8.03 


16.07 


8.10 


18 


19 


17.03 


8.33 


17.04 


8-. 40 


17.00 


8.48 


16.97 


8.55 


19 


20 


17.98 


8.77 


17.94 


8.85 


17.90 


8.92 1 


17.86 
18.75 


9.00 


20 
21 


21 


18.87 


9.21 


18.83 


9.29 


18.79 


9.37 


9.45 


22 


19.77 


9.64 


19.73 


9.73 


19.09 


9.82 


19.65 


9.90 


22 


23 


20.67 


10.08 


20.63 


10.17 


20.58 


10.26 


20.54 


10.35 


23 


24 


21.57 


10.52 


21.52 


10.61 


21.48 


10.71 


21.43 
22.32 


10.80 


24 


25 


22.47 


10.96 


22.42 


11.06 


22.37 


11.15 


11.25 


25 


26 


23.37 


11.40 


23.32 


11.50 


23.27 


11.00 


123.22 


11.70 


26 


27 


24.27 


11.84 


24.22 


11.94 


24.16 


12.05 


24.11 


12.15 


27 


28 


25.17 


12.27 


25.11 


12.38 


25.06 


12.49 


25.00 


12.60 


28 


29 


26.06 


12.71 


26.01 


12.83 


25.95 


12.94 


25.90 


13.05 


29 


30 


26.96 


13.15 


26.91 


13.27 


26.85 
27.74 


13.39 
13.83 


26 . 79 


13.50 1 30 1 


31 


27.86 


13.59 


27.80 


13.71 


27.68 1 13.95 


31 


32 


28.76 


14.03 


28.70 


14.15 


23.64 


14.28 


28.. 58 


14.40 


32 


33 


29.66 


14.47 


29.60 


14.60 


29.53 


14.72 


29.47 


14.85 


33 


34 


30.56 


14.90 


30.49 


15.04 


30.43 


15.17 


30.36 


15.. 30 


34 


35 


31.46 


15.34 


31.39 


15.48 


31.32 


15.62 


31.25 


15.75 


35 


36 


32.36 


15.78 


.32.29 


15.92 


32.22 


16.06 


32.15 


16.20 


36 


37 


33.26 


16.22 


.33.18 


16.36 


33.11 


16.51 


l?3.04 


10.65 


37 


38 


34.15 


16.66 


34.08 


16.81 


34.01 


16.96 


33.93 


17.10 


38 


39 


35 .05 


17.10 


34.98 


17.25 


34.90 


17.40 


34.83 


17.55 


39 


40 


35.95 


17.53 


35.87 


17.69 


35.80 


17.85 
18.29 


35.72 


18.00 


40 


41 


36.85 


17.97 


36.77 


18.13 


36.69 


36.61 


18.45 


41 


42 


37.75 


18.41 


37.67 


18.58 


37.59 


18.74 


37.51 


18.90 


42 


43 


38.65 


18.85 


38.57 


19.02 


3S.48 


19.19 


38.40 


19.35 


43 


44 


39.55 


19.29 


39.46 


19.46 


39.38 


19.63 


i39.29 


19.80 


44 


45 


40.45 


19.73 


40.36 


19.90 


40.27 


20.08 


40.18 


20 . 25 


45 


46 


41.34 


20.17 


41.26 


20.35 


41.17 


20.53 


41.08 


20.70 


46 


47 


42.24 


20.60 


42.15 


20.79 


42.06 


20.97 


41.97 


21.15 


47 


48 


43.14 


21.04 


43.05 


21.23 


42.96 


21.42 


42.86 


21.60 


48 


49 


44.04 


21.48 


43.95 


21.67 


43.85 


21.86 


43.76 


22.05 


49 


50 

5 


, Ai A4. 


' 21.92 


44.84 


22.11 


44.75 


22.31 


44^5_i 22.50 


5(> 


Dcp. 


Lat. 


Dep. 

63| 


Lat. 
Deg. 


Dep. 


Lat. 


Dep. 


Lat. 


1 ^ 


64 


Deg. 


63^ Doer. 


63t Deg. 



TfiAVERSE TABLE. 



125 



-3 

So' 

p 

-1 

52 
53 

54 
55 
5 3 
57 
53 
59 
60 


26 Deg. 


261 Deg. 


1 26^ Deg. 


2ex 


Deg. \ a 


J.at, 1 Dep. 


Lat. 


Dep. 


! Lat. 1 Dep. 

1 i 

45.64' 22.76 

46.54 23.20 

'47.43; 23.65 

,48.33 24.09 

'49.22 24.54 

50.12 24.09 

.51.01,25-43 

51.91 25 S3 

52.80: 26.. 33 

,53.70 26-77 

1.54.59 ' 27.22 

155.49 1 27.66 

56.33 ! 23.11 

57.28 23.56 

58.17 29.00 

59.07 29.45 

59.96 29.90 

60.36 30.34 

61.75 30.79 

62.65 31.23 


Lat, 


Dop. 1 i 

22.90 ' 51 
23.41 5'Z\ 
23.83 53 
24.31 5i 

24.76 1 55 
25.21 ! 56 
25.66 i 57 
26.11 : 53 
26.-56 1 59 
27.01 i 60 


45.84 1 22.36 : 
46.74 122.80 
47.64 i 23.23 
43.53! 23.67 
49.43: 24.11 
50.33 ■ 24.55 
51.23, 24.99 
52.13 125.43 
53.03 ! 25.86 
53.93:26.30 


45.74 
46.64 
47.53 
48.43 
49.33 
50.22 
51.12 
52.02 
52.92 
53.81 


22.56 
23.00 
23.44 
23.83 
24.33 
24.77 
25.21 
25.65 
26.09 
26.54 


46 . 54 
46.43 
47.33 

48 22 
49.11 
50.01 
.50.90 
51.79 
52.69 
53.53 


61 
62 
63 
64 
65 
66 
67 
63 
C9 
70 


54.33 23.74 
55.73 27.13 
56.62 27.62 
57.52 23.06 
53.42 23.49 
59.32 23.93 
60.22 29.37 
01.12 29.81 
62.02 30.25 
62.92 30.69 


154.71 1 26.93 
. 55.61 ! 27.42 
56.C0; 27.88 
57.40; 28.31 
53.30' 23.75 
59.19; 29.19 
60.09 1 29.63 
60.99 30.03 
61.83 30.52 
62.73 30.95 


54,47 27.46 ^ 61 
5-5.36 ' 27.91 ' 62 
56.26 ; 23.36 [ 63 
57.15 1 23.31 64 
53.04 29.26 65 
53.94 29.71 ' 66 
59.83 30.16 i 67 
60.72' 30.61 1 63 
61.63 JGl. 06 69 
62.51 131.51 1 70 


71 63.81 

72 64.71 

73 65.61 

74 ; 66.51 

75 ; 67.41 

76 63.31, 

77 i 69.21 
73 70.11 
ro 71.00 
SO 71.90 


31.12 1 63.63, 31.40 
31.56 164.57; 31.84 
32.00 165.47; 32.29 
32.44 1 66.37, .32.73: 
32.83 67.27! 33. 17 
33..32| 63.16 i 33.61 
33.75 '69.06 ! 34.06 
34.19 69.96 i 34.50 
34.63 70.85; 34.94 
35.07 j 71.75' 35.38 


63.54 31.63 
64.44 32.13 
65.33 32.57 
66.23! 33.02 
67. 12 '33.46 
63.01 33.91 
63.91 34.36 
69.80 34.30 
70.70 35.25 
71.59, 35.70 


63.40 
64.29 
65.19 
66.03 
66.97 
67.87 
63.76 
69.65 
70.55 
71.44 
72.33 
73.22 
74.12 
75.01 
75.90 
76.80 
77.69 
78.58 
79.48 
80.37 


31.96 - 71 
32.41 72 
32.36 , 73 
33.31 1 74 
33.76 1 75 
34.21 i 76 
34.66 77 
35.11 . 73 
35.56 79 
36.01 SO 


81 1 72.30, 

82 73.70 

83 74.60' 

84 75.50 

85 76.40 

86 77.30 

87 73.20 

88 79.09. 

89 79.99 

90 80.89 


35.51 
35.95 
36.33 
36.82 
37.26 
37.70 
38.14 
33.53 
.39.01 
39.45 


172.65 

73.54 

74.44 

75.34 

76.23 

77.13 

178.03 

i 78.92 

179.82 

80.72 


35.83: 

36.27' 

.36.71 ! 

37.15 

37.59 

33.04; 

33 43 

33.92 

39.36 

39.81 


72.49' 36.14 
73.33 36.59 
74.28 1 37.03 
75.17: 37.43 
76.07' 37.93 
76.96' 38.37 
77.86 .38.82 
73.75' 39.27 
79.65 39.71 
30.54 40.16 
81.44 40.60 
82.33 41.05 
83.23 41.50 
84.12 41.94 
85.02 42.39 
85.91 42.83 
86.81 43.23 
37.70 43.73 
83.60 44.17 
89.49,4.1.62 


36.46 : 81 
36.91 i 82 
37.36 83 
37.81 . 84 
33.26 ' 85 
33.71 . 86 
39.16 87 
39.61 , S3 
40.06 89 
40.51 ; 90 


91 
92 
93 
94 
95 
96 
97 
98 
99 
100 

§ 
c 
2 

m 

Q 


81.79 
82.69 
83.59 
84.49 
85.39 
86.23 
87.18 
88.03 
88.93 
89.83 


39.89 
40.33 
40.77 
41.21 
41.65 
42.03 
42.52 
42.96 
43.40 
43.84 


181.62 
82.51 

; 83.41 
84.31 
85.20 

,86.10 
87.00 

,87.89 

,88.79 
89. 6S 


40.25 
40.69 
41.13 
41.53 
42.02 
42.46 
42.90 
43.34 
43.79 
44.23 


81.26 40.96 91 
82.15 41.41 92 
83.05 41.80 93 
83.94 42.31 ' 94 
84.83 42.76 95 
85.73 43.21 96 
86.62 43.66 97 
87.51 44.11 9S 
83.40 44.56 99 
89.30 45.01 100 

Dep.; Lat. S 
, 63i Deg. Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. ! Lat. 
63| Deg. 


64 Deg. 


63J Dog. 



126 



TEAVEKSE TABLE. 



5 

Si 


27 Deg. 


27iDeg. 


27^ Deg. 1 


27i Deg. 

1 


1 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 


Lat 


Dep. 


"n 


0.8& 0.45 


0.89 


0.46 1 


0.89 


j.4fi 


C.K% 


G.47 


1 


2 


1.78 0.91 


1.78 


0.92 1 


1.77 


0.92 


1.77 


0.93 


2 


3 


2.67! 1.36 


2.67 


1.37 1 


2.66 1.3y! 


{! G5 


1.40 


3 


4 


3.56 i 1.82 


3.. 56 


1.83 1 


3..^5 


1.85 i 


L.Ci 


1.86 


4 


5 


4.4.;! 2.27 


4.45 


2.29 


4.44 


2.31 1 


4.42 


2.33 


5 


6 


5.35 2.72 


5.33 


2.75 


5.32 


2.77 


5.31 


2.79 


G 


7 


6.24 3.18 


6.22 


3.21 1 


^ 6.21 


3.23 


6.19 


3.26 


7 


8 


7.13 3.63 


7.11 


3.66 5 


7.10 


3.69 


7.08 


3.72 


8 


9 


8.02; 4.09 


8.00 4.12 1 


7.98 


4.16' 


7.96 


4.19 


S 


10 

11 


8.91 ! 4.54 
9.80 4.99 


8.89 4.58 


8.87 


4.62 1 


8.85 


4.66 
5.12 


10 
11 


9.78 5.04 1 


9.76 


5.08 1 


9.73 


12 


10.69 


5.45 


10.67 


5.49 


10.64 


5.54' 


10.62 


5.. 59 


12 


13 


11.. 58 


5.90 


11.56 


5.95 1 


11.53 


6.00! 


U..50 


6.05 


13 


14 


12.47 


6.36 


12.45 


6.41 1 


12.42 


6.46 


12.39 


6.52 


14 


15 


13.37 


6.81 


13.34 


6.87 


13.31 


6.93 


13.27 


6.9S 


15 


it- 


14.26 


7.26 


14.22 


7.33 


14.19 


7.39 


14.16 


7.45 


16 


17 


15.15 


7.72 


15.11 


7.78 


15.08 


7.85 1 


15.04 


7.92 


17 


18 


16.04 


8.17 


16.00 


8.24 1 


15.97 


8.31 


15.93 


8. .38 


18 


19 


16.93 1 8.63 


16.89 


8.70 1 


16.85 


8.77 


16.81 


8.85 


19 


2« 

21 


17.82 
18.71 


9.08 
9.53 


17.78 


9.16 


17.74 
18.63 


9.23 


17.70 


9.31 


20 

21 


18.67 


9.62! 


9.70 


18.58 


9.78 


22 


19.60 


9.99 


19.56 


10.07 1 


19.51 


10.16 


19.47 


10.24 


22 


23 


20.49 


10.44 


20.45 


10.53 


20.10 


10.62 1 


20.35 


10.71 


23 


24 


21.38 


10.90 


21. .34 


10.99 


21.29 


11.08: 


21.24 


11.17 


24 


25 


22.28 


11.35 


22.23. 


11.45 


22.18 


11.54 


22.12 


n.64 


25 


26 


23.17 


11.80 


23.11 


11.90! 


23.06 


12.01 


23.01 


12.il 


26 


27 


24.06 


12.26 


i 24.00 


12.36 


23.95 


12.47! 


23.89 


12.57 


27 


28 


24.95 


12.71 


24.89 


12.82 


24.84 


12.93 


24.78 


13.04 


28 


29 


25.84 


13.17 


1 25.78 


13.28 


25.72 


13.39 


25.66 


13.50 


29 


30 
-31 


26.73 


13.62 


126.67 
27.56 


13.74 
14.19 


26.61 


13.85 


26.55 


13.97 


30 
31 


27.62 


14.07 


27.50 


14.31 


27.43 


14.43 


32 


28.51 


14.53 


28.45 


14.65 


28.38 


14.78 


28.32 


14.90 


32 


33 


29.40 


14.98 


29.34 


15.11 


29.27 


1.'..24 


29.20 


15.37 


33 


34 


30.29 


15.44 


30.23 


15.57 


.30.16 


•5.70 


30.09 


15.83 


34 


35 


31.19 


15.89 


31.12 


16.03 


31.05 


16.16 


30.97 


16.30 


35 


36 


32.08 


16.34 


32.00 


16.48 


31.93 


10.62 


i • .86 


16.76 


36 


37 


32.97 


16.80 


32.89 


16.94 


32.82 


17.08 


Si. 74 


17.23 


37 


38 


33.86 


17.25 


33.78 


17.40 


33.71 


17.55 


33.63 


17.69 


38 


39 


34.75 


17.71 


34.67 


17.86 


34.59 


18.01 


34.51 


18.16 


39 


40 


35.64' 18.16 !: 35.56 


18.31 


35.48 


18.47 


35.40 


18.62 


40 


41 


36.53 18.61 ! 36.45' iS.77 


36.37 


18.93 


36.28 


19.09 


41 


42 


37.42 


19.07 37.34 
19.52 ! 38.23 


19.23 


37.25 


19.39 


37.17 


19.56 


42 


43 


38.31 


19.69 


38.l4j 19.86 


38.05 


20.02 


43 


44 


39.20 


19.98 


139.12 


20.15 


39.03 20.32 


33.94 


20.49 


44 


45 


40.10 


20.43 


140.01 


20.60 


39.92 20.78 


39.82 


20.95 


45 


46 


40.99 


20.88 


140.89 


21.06 


140.80' 21.24 


40.71 


21.42 


46 


47 


41.88 i 21.34 


41.78 


21.52 


41.691 21.70 


41.59 


21.88 


47 


4S 


42.77 21.79 


42.67 


21.98 


42.. 58 


! 22.16 


42.48 


22.35 


48 


49 


43.66 ,22.25 


43.56 


22.44 


43.45 


22.63 


43.36 


22.82 


49 


50 


44.55 ! 22.70 144.45 


22.89 


44.35 


23. Oj 


4t.25 
Dep. 


23 28 
Lat. 


50 

ci 

o 

1 


Dep. 1 Lat. 


Dep. 


Lat, 


Dep. 


Lat 


.2 
Q 


II 
63 Deg. 621 Deg. 


621 Deg 


6'* 


Deg. 



TRAVERSE TABLE. 



127 



p 


27 Deg. 


27i Deg. 


27i Deg. 


27| Deg. 


a 

a 


3 


Lat. 


Dep. 


1 Lat. 1 Dep. 


Lat. 


Dep. i 


Lat. Dep. 


51 Il5.4i 123.15 


45.34 23.35 


'45.24 


23.55 


45.13 1 23.75 


'sT 


62 


16.33 23.61 


'46.23 ,23.81 ; 48.12 


24.01 


46.02 124.21 


52 


53 


47.22 24.06 


47.12 24.27 47.01 


24.47 


46.90! 24.68 


53 


54 


4S.11 24.52 


43.01 24.73 47.90 


24.93 


47.79 1 25.14 


54 


55 


49.01 24.97 


43.90; 25,18 43.79 


25.40; 


48.67 25.61 


55 


56 


49.90 25.42 


49.73 I 25.64 49.67 


25.86' 


49.56 26.07 


56 


57 


50.79 1 25.83 


' 50.67 26.10 50.56 


26.32 


.50.44 126.54 


57 


58 


51.63 1 26.33 


51.56 26.56 51.45 


26.73 


51.33 27.01 


58 


59 


52.57 126.79 


52.45 27.01 ,52.33 


27.24 


52.21 127.47 


59 


60 
61 


53.46' 27.24 
54.35 27.69 


1 53.34 27.47 
54.23 27.93 


,53.22 


27.70 1 


.53.10 127.94 
53.98 1 23.40 


60 
61 


54.11 


23.17 


62 


55.24 28.15 


55.12, 23.39 54.99 


23.63 


.54.87 j 23.37 


62 


63 


56.13: 23.60 


56.01 ! 23.85 55.83 


29.09 


55.75 29.33 


63 


64 


57.02 


29.06 


56.90 29.30 56.77 


29.55, 


56.64 29.80 


64 


65 


57 92 


29.51 


57.79 29.76 57.66 


30.01 


57.52 30.26 


65 


66 


58.81 


29.96 


, 53.63 30.22 53.54 


30.43 


53.41 130.73 


66 


67 


59.70 


.30.42 


59.56 ; 30.68 159.43 


30.94 


59.29 31.20 


67 


63 


60.59 


30.87 


60.45 31.14 


160.33 


31.40 


60.18 31.66 


68 


69 


61.48 


31.33 


: 61.34: 31.59 


161.20 


3].86' 


61.06 32.13 


69 


70 
71 


62.37 


31.78 


i 62.23: 32.05 


162.09 


32.32 


61.95 32.59 


70 
71 


63.26 


32.23 , 6?. 12 ,32.51 162.98 


32 . 73 


62.83 133.06 


72 


64.15 


32.69 


[G4.01 32.97 : 63.86 


33.25 


63.72 1 33.52 


72 


73 


65.04 


33.14 


! 64.90 33.42 164.75 


33.71 


64.60 33.99 


73 


74 


65.93 


33.60 


1 65.79 133.83 '65.64 


34.17 


65.49 134.46 


74 


75 


66.83 


34.05 


66.63 


34.34 1 66.53 


34.63 


66.37 1 34.92 


75 


76 


67.72 


34.50 


: 67.57 


34.80 ! 67.41 


35.09 


67.26 35.39 


76 


77 


63.61 


34.96 


; 68.45 


35.26 163.30 


35.55 


63.14 35.85 


77 


78 


69.50 


35.41 


1 69.34 


35.71 I 69.19 136.02' 


69.03 136.32 


78 


79 


70.39 


35.87 


1 70.23 136.17 11 70.07 


36.43 


69.91 136.73 


79 


80 
81 


71.28 


36.32 
36.77 


71. 12 j 36.63 I: 70.96 


36.94 
37.40 


70.80 137.25 


80 
81 


72.17 


72.01 


37.09 Ij 71.85 


71.63 


37.71 


82 


73.06 


37.23 


72.90 


37.55 1 72.73 


37.86! 


72.57 


33.13 


82 


83 


73.95 


37.68 


73.79 


38.00 ij 73.62 


33.33 


73.45 


33.65 


83 


84 


74.84 


38.14 


74.68 


33.46 ii 74.51 


33.79 


74.34 1 39.11 


84 


85 


V5.74 


38.59 


75.57 


33.92 Ii 75.40 


39.25 


75.22 


39.58 


85 


86 


76.63 


39.04 


76.46 


39.38 i 76.23 


39.71 ' 


76.11 


40.04 


86 


87 


77.:.2 139.50 


77.34 


39.83 77.17 


40.17 


76.99 


40.51 


87 


88 


78.41,39.95 


78.23 


40.29 1,78.06 140.63 


77.88 


40.97 


88 


89 


79.30:40.41 


79.12 i 40.75 ji 78.94 141.10 


73.76 


41.14 


89 


90 
91 


80.19' 10.86 
81.08 41.31 i 


SO. 01 i41.21 
80.90 ,41.67 


i 79.83 141.56 


79.65 


41.91 


90 
91 


180.72,42.02 


80.53 


42.37 


92 


81 97 41.77 1 


81.79 42.12!; 81.60 '42.48 


81.42 i 42.84 


92 


93 


82.86 42.22 1 


82.68 42.53 i 82.49 42.94 


82.30 i 43.30 


93 


94 


83.75 42.68 t 


83.57 43.04 I 83.33 43.40 


83.19 


43.77 


94 


95 


84.65 43.13 


84.46 ; 43.50 | 84.27 43.87 


84.07 


44.23 


95 


96 


85.54 43.. 53 


85.35 '43.96 85.15 144.33 


84.96 


44.70 • 


96 


97 


86.43 44.04^ 


86.23 i 44.41 


86.04 1 44.79 


85.84 


45.16 


97 


9S 


87.32 44.49- 


87.12 144.87 


86.93 145.25 


86.73! 45.63 


98 


99 


83.21 44.9') 1 


88.01 


45.33 i 


87.81 45.71 i 


87.61146.10 


99 


iOO 

i 

3 


89.10 
Dep. 


45.40 i 


88.90 


45.79 


88.70 


46.17; 


88.50 146.56. 
Dep. 1 Lat, , 


100 

.5 


I.at. 


Dep. 


Lat. 


Dep. 


Lat. 


1 


63Deg. 


62i Deg. 


621 Deg. , 


62i 


Deg, 



128 



TRAVERSE TARLE. 



1' 

p 


23 Deg. 


28i Beg. 


28|- Deg. 


281 Deg. 


a.' 

'"l 


Lat. 


Dep. 


Lat. 

0.88 


Dep. 

0.47 


Lat. 


Dep. 


Lat. 

0.88 


Dep. 

0.48 


"T 


0.88 


0.47 


0.88 


0.48 


2 


1.77 


0.94 


1.76 


0.95 


1.76 


0.95 


1.75 


0.96 


2 


3 


2.65 


1.41 


2.64 


1.42 


2.64 


1.43 


2.63 


1.44 


3 


4' 3.53 


1.88 


3.62 


1.89 


3.52 


1.91 


3.51 


1.92 


4 


5 : 4.41 


2.35 


4.40 


2.37 


4.39 


2.39 


4.38 


2.40 


5 


6 : 5.30 


2.82 


5.29 


2.84 


5.27 


2.86 


5.26 


2.89 


6 


7 6.18 


3.29 


6.17 


3.31 


6.15 


3.34 


6.14 


3.37 


7 


8 


7.06 


3.76 


7.05 


3.79 


7.03 


3.82 


7.01 


3.85 


8 


9 


7.95 


4.23 


7.93 


4.26 


7.91 


4.29 


7.89 


4.33 


9 


10 
11 


8.83 


4.69 


8.81 
9.69 


4.73 
5.21 


8.79 
9.67 


4.77 
5.25 


8.77 


4.81 


10 
11 


9.71 


5.16 


9.64 


5.29 


12 


10.60 


5.63 


10.57 


5.68 


10.55 


5.73 


10.52 


5.77 


12 


13 


11.48 


6.10 


11.45 


6.15 


11.42 


6.20 


11.40 


6.25 


13 


14 


12.36 


6.57 


12.33 


6.63 


12.30 


6.68 


12.27 


6.73 


14 


15 


13.24 


7.04 


13.21 


7.10 


13.18 


7.16 


13.15 


7.21 


15 


16 


14.13 


7.51 


14.09 


7.57 


14.06 


7.63 


14.03 


7.70 


16 


17 


15.01 


7.98 


14.98 


8.05 


14.94 


8.11 


14.90 


8.18 


17 


18 


15.89 


8.45 


15.86 


8.52 


15.82 


8.59 


15.78 


8.66 


18 


19 


16.78 


8.92 


16.74 


8.99 


16.70 


9.07 


16.66 


9.14 


19 


30 
21 


17.66 


9.39 


17.62 


9.47 


17.58 
18.46 


9.54 
10.02 


17.53 


9.62 


20 
21 


18.54 


9.86 


18.50 


9.94 


18.41 


10.10 


22 


19.42 


10.33 


19.38 


10.41 


19.33 


10.50 


19.29 


10.58 


22 


23 


20.31 


10.80 


20.26 


10.89 


20.21 


10.97 


20.16 


11.06 


23 


24 


21.19 


11.27 


21.14 


11.36 


21.09 


11.45 


21.04 


11.54 


24 


25 


22.07 


11.74 


22.02 


11.83 


21.97 


11.93 


21.92 


12.02 


25 


26 


22.96 


12.21 


22.90 


12.31 


22.85 


12.41 


22.79 


12.51 


26 


27 


23.84 


12.68 


23.78 


12.78 


23.73 


12.88 


23.67 


12.99 


27 


28 


24.72 


13.15 


24.66 


13.25 


24.61 


13.36 


24.55 


13.47 


28 


29 


25.61 


13.61 


25.55 


13.73 


25.49 


13.84 


25.43 


13.95 


29 


30 


26.49 


14.08 


26.43 


14.20 


26.36 
27.24 


14.31 
14 79 


26.30 


14.43 


30 
31 


31 


27.37 


14.55 


27.31 


14.67 


27.18 


14.91 


32 


28.25 


15.02 


28.19 


15.15 


28.12 


15.37 


28.06 


15.39 


32 


33 


29.14 


15.49 


29.07 


15.62 


29.00 


15. 7e 


28.93 


15.87 


33 


34 


30.02 


15.96 


29.95 


16.09 


29.88 


16.22 


29.81 


16.35 


34 


35 


30.90 


16.43 


30.83 


16.57 


30.76 


16.70 


30.69 


16.83 


35 


36 


31.79 


16.90 


31.71 


17.04 


31.64 


17.18 


31.56 


17.32 


36 


37 


32.67 


17.37 


32.59 


17.51 


32.52 


17.65 


32.44 


17.80 


37 


38 


33.55 


17.84 


33.47 


17.99 


33.39 


18.13 


33.32 


18.28 


38 


39 


34.43 


18.31 


34.35 


18.46 


34.27 


18.61 


34.19 


18.76 


39 


40 


35.32 


18.78 


35.24 


18.93 


35.15 


19.09 


35.07 


19.24 


40 
41 


41 


36.20 


19,25 


36.12 


19.41 


36.03 


19.56 


35.95 


19.72" 


42 


37.08 


19.72 


37.00 


19.88 


36.91 


20.04 


36.82 


20.20 


42 


43 


37.97 


20.19 


37.88 


20.35 


.37.79 


20.52 


37.70 


20. 08 


43 


44 


38.85 


20.66 


38.76 


20.83 


38.67 


20.99 


38.58 


21.16 


44 


45 


39.73 


21.13 


39.64 


21.30 


39.55 


21.47 


39.45 


21.64 


45 


46 


40.62 


21.60 


40.52 


21.77 


40.43 


21.95 


40.33 


22.13 


46 


47 


41.50 


22.07 


41.40 


22.25 


41.30 


22.43 


41.21 


22.61 


47 


48 


42.38 


22.. 53 


42.28 


22.72 


42.18 


22.90 


42.08 


23.09 


48 


49 


43.26 


23.00 


43.16 


23.19 


43.06 


23.38 


42.96 


23.57 


49 


50 

g 
1 


44.15 


23.47 


44.04 


23.67 


43.94 


23.86 


43.84 


24.05 


50 

'1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. 


62 1 


)eg. 


61| Deg. 


61^ Deg. 


6U Deg. 



TRAVERSE TABLE. 



129 



OD 

13 
O 

a 


28 Deg. 


28i Deg. 


28i Deg. 


281 Deg. 


'rr. 

i 

51 


Lat. 


Dep. 


Lat. 
44.93 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


45.03 


23.94 


24.14 


44.82 i 24.34 


44.71 


24.53 


52 


45.91 


24.41 i 


45.81 24.61 i 


45.70 124.81 


45.59 


25.01 


52 


53 


46.80 


24.88 1 


46.69 


25.09 


46.58 1 25.29 


46.47 


25.49 


53 


54 


47.68 


25.35! 


47.57 


25.56 


47.46 125.77 


47.34 


25.97 


54 


55 


48.56 


25.82' 


48.45 


26.03 


48.33 26.24 


48.22 


26.45 


55 


56 


49.45 


26.29 
26.76 


49.33 


26.51 


49.21 '26.72! 


49.10 


26.94 


56 


57 


50.33 


50.21 


26.98 


50.09 


27.20 


49.97 


27.42 


57 


58 51.21 


27.23 


51.09 


27.45 


50.97 


27.68 


50.85 


27.90 


58 


59 


52.09 


27.70 1 


51.97 


27.93 


51.85 


28.15 


51.73 


28.38 


59 


60 
61 


52.93 


28.17 i 


52.85 1 28.40] 


.52.73 


28.63 


52.60 


28.86 


60 
61 


53.86 


28.64 


53.73 


23.87 


53.61 


29.11 


53.48 


29.34 


62 


54.74 


29.11 


54.62 


29.35 


54.49 


29.58 


54.36 


29.82 


62 


63 


55.63 


29.58 


55.50 


29.82 


55.37 


30.06 


55.23 


30.30 


63 


64 


56.51 


30.05 


56.38 


30.29 


50.24 


30.54 


56.11 


30.78 


64 


65 


57.39 


30.52 


57.26 


30.77 


57.12 


31.02 


56.99 


31.26 


65 


66 


58.27 


30.99 


58.14 


31.24 


58.00 


31.49 


57.86 


31.75 


66 


67 


59.16 


31.45 


59.02 


31.71 


58.88 


31.97 


58.74 


32.23 


67 


68 


60.04 


31.92 


59.90 


32.19 


59.76 


32.45 


59.62 


32.71 


68 


69 


60.92 


32.39 


60.78 


32.60 


60.64 


32.92 


60.49 


33.19 


69 


70 
71 


61.81 


32.86 
33.33 


61.60 


33.13 


61.52 


33.40 


61.37 


33.67 


70 

71 


62.69 


62.54 


33.61 


62.40 


33.88 


62.25 


34.15 


72 


63.57 


33.80 


63.42 


34.08 


63.27 


34.36 


63.12 


34.63 


72 


73 


64.46 


34.27 


64.30 


34.55 


!64.15 


34.83 


64.00 


35.11 


73 


74 


65.34 


34.74 


65.19 


35.03 


65.03 


35.31 


64.88 


35.59 


74 


75 


66.22 


35.21 


66.07 


35.50 


65.91 


35.79 


i 65.75 


36.07 


75 


76 


67.10 


35.68 


66.95 


35.97 


66.79 


36.26 


166.63 


36.56 


70 


77 


67.99 


36.15 


67.83 


36.45 


67.67 


36.74 


1 67.51 


37.04 


77 


78 


68.87 


36.62 


68.71 


36.92 


68^55 


37.22 


! 68.38 


37.52 


78 


79 


69.75 


37.09 


69.59 


37.39 


69.43 


37.70 


69.26 


38.00 


V9 


80 
81 


70.64 


37.56 


70.47 


37.87 


70.31 


38.17 


70.14 


38.48 
38.96 


80 
81 


71.52 


38.03 


71.35 


38.34 


71.18 


38.65 


71.01 


82 


72.40 


38.50 


72.23 


38.81 


72.06 


39.13 


71.89 


39.44 


82 


83 


73.28 


38.97 


73.11 


39.29 


72.94 


39.60 


72.77 


39.92 


83 


84 


74.17 


39.44 


73.99 


39.76 


73.82 


40.08 


73.64 


40.40 


84 


85 


75.05 


39.91 


74.88 


40.23 


74.70 


40.56 


74.52 


40.88 


85 


86 


75.93 


40.37 


75.76 


40.71 


75 58 


41.04 


75.40 


41.36 


86 


87 


76.82 


40.84 


76.64 


41.18 


76.46 


41.51 


76.28 


41.85 


87 


88 


77.70 


41.31 


77.52 


41.65 


77.34 


41.99 


77.15 


42.33 


88 


89 


78.58 


41.78 


78.40 


42.13 


78.21 


42.47 


78.03 


42.81 


89 


90 
91 


79.47 


42.25 


79.28 


42.60 


79.09 


42.94 


78.91 


43.29 


90 
91 


80.35 


42.72 


80.16 


43.07 


79.97 


43.42 


79.78 


43.77 


92 


81.23 


43.19 


81.04 


43.55 


80.85 


43.90 


80.66 


44.25 


92 


93 


82.11 


43.66 


81.92 


44.02 


81.73 


44.38 


81.54 


44.73 


93 


94 


183.00 


44.13 


82.80 


44.49 


82.61 


44.85 


82.41 


45. PI 


94 


95 


83.88 


44.60 


83.68 


44.97 


83.49 


45.33 


83.29 


45.19 


95 


95 


84.78 


45.07 


84.57 


45.44 


84.37 


45.81 


84.17 


46.17 


90 


97 '85.65 


45.54 


85.45 


45.91 


85.25 


46.28 


85.04 


46.66 


97 


98 


186.53 


46.01 


86 33 


46.39 


86.12 


46.76 


85.92 


47.14 


98 


99 


87.41 146.48 


87.21 


46.86 


87.00 


47.24 


86.80 


47.62 


99 


100 

§ 
a 
S 
.3 

Q 


88.29 |46.95 


88.09 


47.33 


87.88 


47.72 


87.67 


48.10 


100 

i 

c 
a 


Dep. Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


1 

1 62 Deg. 


61| Deg. 


eU Deg. 


6ii Deg. 

1 



130 



TRAVERSE TAELE. 



§ 
1 


29 Deg. 

1 


2n Deg. 


29i Deg. 


29J Deg. 




Lat. 
"0787 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.48 


0.87 


0.49 


0.87 


0.49 


0.87 


0..'J0 


2 


1.75 


0.97 


1.74 


0.98 


1.74 


0.98 


1.74 


0.99 


2 


3 2.62 f 


1.45 


2.62 


1.47 


2.61 


1.48 


2. GO 


1.49 


3 


4 


3.50 


1.94 


3.49 


1.95 


3.48 


1.97 


3.47 


1.98 


4 


5 


4 37 


2.42 


4.36 


2.44 


4.35 


2.46 


4.34 


2.48 


5 


6 


5.25 


2.91 


6.23 


2.93 


5.22 


2.95 


5.21 


2.98 


6 


7 


6.12 


3.39 


0.11 


3.42 


6.09 


3.45 


6.08 


3.47 


7 


8 7.00 ( 


3.88 


6.98 


3.91 


6.96 


3.94 


6.95 


3.97 


8 


9 


7.87 


4.36 


7.85 


4.40 


7.83 


4.43 


7.81 


4.47 


9 


10 
11 


8.75 
9.62 


4.85 
5.33 


8.72 


4.89 


8.70 


4,92 


8.68 


4.90 


10 
11 


9.60 


5.37 


9.. 57 


5.42 


9.55 


5.46 


12 


10.50 


5.82 


10.47 


5.88 


10.44 


5.91 


10.42 


5.95 


12 


13 


11.37 


6.30 


11.34 


6.35 


11.31 


6.40 


11.29 


6.45 


13 


14 


12.24 


6.79 


12.21 


6.84 


12.18 


6.89 


12.15 


6.95 


14 


15 


13.12 


7.27 


13.09 


7.33 


13.06 


7.39 


13.02 


7.44 


15 


16 


13.99 


7.76 


13.96 


7.82 


13.93 


7.88 


13.89 


7.94 


16 


17 


14.87 


8.24 


14.83 


8.31 


14.80 


8.37 


14.76 


8.44 


17 


18 


15.74 


8.73 


15.70 


8.80 


15.67 


8.86 


15.63 


8.93 


18 


19 


16.62 


9.21 


16.58 


9.28 


16.54 


9.36 


16.50 


9.43 


19 


20 


17.49 


9.70 
10.18 


17.45 
18.32 


9.77 
10.26 


17.41 
18.28 


9.85 
10734 


17.30 


9.92 


20 
21 


21 


18.37 


18.23 


10.42 


22 


19.24 


10.67 


19.19 


10.75 


19.15 


10.83 


19.10 


10.92 


22 


23 


20.12 


11.15 


20.07 


11.24 


20.02 


11.33 


19.97 


11.41 


23 


24 


20.99 


11.64 


20.94 


11.73 


20.89 


11.82 


20.84 


11.91 


24 


25 


21.87 


12.12 


21.81 


12.22 


21.76 


12.31 


21.70 


12.41 


25 


26 


22.74 


12.60 


22.68 


12.70 


22.63 


12.80 


22.57 


12.90 


26 


27 


23.61 


13.09 


23.56 


13.19 


23.50 


13.30 


23.44 


13.40 


27 


28 


24.49 


13.57 


24.43 


13.68 


24.37 


13.79 


24.31 


13.89 


28 


29 


25.36 


14.06 


25.30 


14.17 


25.24 


14.28 


25.18 


14.39 


29 


30 


26.24 


14.54 


26.17 


14.06 


26.11 
26.98 


14.77 
15.27 


26.05 


14.89 


30 
31 


31 


27.11 


15.03 


"27.05 


15.15 


26.91 


15.38 


32 


27.99 


15.51 


27.92 


15.64 


27.85 


15.76 


27.78 


15.88 


32 


33 


28.86 


16.00 


28.79 


16.12 


28.72 


16.25 


28.65 


16.38 


33 


34 


29.74 


16.48 


29.66 


16.61 


29.59 


16.74 


29.52 


16.87 


34 


35 


30.61 


16.97 


30.54 


17.10 


30.46 


17.23 


30.39 


17.37 


35 


36 


31.49 


17.45 


31.41 


17.59 


31.33 


17.73 


31.26 


17.86 


36 


37 


32.. 36 


17.94 


32.28 


18.08 


32.20 


18.22 


32.12 


18. .36 


37 


38 


33.24 


18.42 


33.15 


18.57 


33.07 


18.71 


32.99 


18.86 


38 


39 


34.11 


18.91 


34.03 


19.06 


33.94 


19.20 


33.86 


19.35 


39 


40 
41 


34.98 


19.39 


34.90 


19.54 


34.81 


19.70 


34.73 


19.85 


40 
41 


35.86 


19.88 


35.77 


20.03 


35.68 


20.19 


35.60 


20.34 


42 


36.73 


20.36 


36.64 


20.52 


36.55 


20.68 


36.46 


20.84 


42 


43 


37.61 


20.85 


37,52 


21.01 


37.43 


21.17 


37.33 


21.34 


43 


44 


38.48 


21.33 


38.39 


21.50 


38.30 


21.67 


38.20 


21.83 


44 


45 '39.36 


21.82 


39.26 


21.99 


39.17 


22.16 


39.07 


22.33 


45 


46 1 40.23 


22.30 


40.13 


22.48 


40.04 


22.65 


39.94 


22.83 


46 


47 


41.11 


22.79 


41.01 


22.97 


40.91 


23.14 


40.81 


23.32 


47 


48 


41.98 


23.27 


41.88 


23.45 


41.78 


23,68 


41.67 


23.82 


48 


•^9 


42.86 


23.70 


42.75 


23.94 


42.65 


24.13 


42.54 


24.31 


49 


50 


i3.73 


24.24 
Lat. 


43.62 


24.43 


43.52 


24.62 


43.41 


_24.^1 


50 


8 
a 


Dep. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


61 


Deg. 


601 Deg. 


eOh Deg. 


60i Deg. 


1 



TRAVERSE TABLE. 



131 



o 

* 1 


29 Beg. 


29i Deg. 


29A Deg. 


291 Deg. 


D 
"51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 
25731 


"51 144.61 1 


24.73 1 


44.50 


24.92 


44.39 


■25. IT 


44.28 


62 


45.48 


25.21 


45.37 


25.41 


45.26 


25.61 


45.16 


25.80 


62 


63 


46.35 


25.69 


46.24 


25.90 


46.13 


26.10 


46.01 


26.30 


53 


d4 


47.23 


26.18 


47.11 


26.39 


47.00 


26.59 


46.88 


26.80 


54 


65 


48.10 


26.66 


47.99 


26.87 


47.87 


27.08 


47.75 


27.29 


65 


56 


48.98 


27.15 


48.86 


27.36 


48.74 


27.68 


48.62 


27.79 


66 


67 


49.85 


27.63 


49.73 


27.85 


49.61 


28.07 


49.49 


28.28 


57 


58 


50.73 


28.12 


50.60 


28.34 


50.48 


28.56 


50.36 


28.78 


58 


59 


51.60 


28.60 


51.48 


28.83 


51.35 


29.05 


61.22 


29.28 


69 


60 
61 


52.48 


29.09 
29.57 


52.35 


29.32 


52.22 


29.55 


52.09 
52.96 


29.77 


60 
61 


53.35 


53.22 


29.81 


53.09 


30.04 


30.27 


62 


54.23 


30.00 


54.09 


30.29 


53.96 


30.63 


53.83 


30.77 


62 


63 


55.10 


30.54 


54.97 


30.78 


54.83 


31.02 


54.70 


31.26 


63 


64 


55.98 


31.03 


.55.84 


31.27 


65.70 


31.62 


65.56 


31.76 


64 


65 


56.85 


31.51 


56.71 


31.76 


56.57 


32.01 


66.43 


32.25 


65 


66 


57.72 


32.00 


57.58 


32.25 


57.44 


32.60 


67.30 


32.75 


66 


67 


.58.60 


32.48 


58.46 


32.74 


58.31 


32.99 


58.17 


33.25 


67 


68 


.59.47 


32.97 


59.33 


33.23 


59.18 


33.48 


69.04 


33.74 


68 


69 


60.35 


33.45 


60.20 


33.71 


60.05 


33.98 


,59.91 


34.24 


69 


70 
71 


61.22 


33.94 


61.07 


34.20 


60.92 


34.47 


60.77 


34.74 


70 


62.10 


34.42 


61.95 


34.69 


61.80 


34.96 


61.64 


35.23 


71 


72 


62.97 


34.91 


62.82 


35.18 


62.67 


35,46 


62.61 


35.73 


72 


73 


63.85 


35.39 


63.69 


35.67 


63.54 


35.95 


63.38 


36.22 


73 


74 


64.72 


35.88 


64.56 


36.16 


64.41 


36.44 


64.25 


36.72 


74 


75 


65.60 


36.36 


65.44 


36.65 


65.28 


36.93 


65.11 


37.22 


76 


76 


66.47 


36.85 


66.31 


37.14 


66.15 


37.42 


66.98 


37.71 


76 


77 


67.35 


37.33 


67.18 


37.62 


67.02 


37.92 


66.86 


3§.21 


77 


78 


68.22 


37.82 


68.05 


38.11 


67.89 


38.41 


67.72 


38.70 


78 


79 


69.09 


38.30 


68.93 


38.60 


68.76 


38.90 


68.59 


39.20 


79 


80 
81 


69.97 
70.84 


38.78 


69.80 


39.09 


69.63 


39.39 


69.46 


39.70 


80 
81 


39.27 


70.67 


39.58 


70.50 


39.89 


70.32 


40.19 


82 


71.72 


39.75 


71.54 


40.07 


71.37 


40.38 


71.19 


40.69 


82 


83 


72.59 


40.24 


72.42 


40.56 


72.24 


40.87 


72.06 


41.19 


83 


84 


73.47 


40.72 


73.29 


41.04 


73.11 


41.36 


72.93 


41.68 


84 


85 


74.34 


41.21 


74.16 


41.53 


73.98 


41.86 


73.80 


42.18 


85 


86 


75.22 


41.69 


75.03 


42.02 


74.85 


42.35 


74.67 


42.67 


86 


87 


76.09 


42.18 


75.91 


42.51 


75.72 


42.84 


75.53 


43.17 


87 


88 


76.97 


42.66 


76.78 


43.00 


76.59 


43.33 


76.40 


43.67 


88 


89 


77.84 


43.15 


77.65 


43.49 


77.46 


43.83 


77.27 


44.16 


89 


90 
91 


78.72 


43.63 


78.52 
79.40 


43.98 
44.46 


78.33 


44.32 


78.14 


44.66 


90 

91 


79.59 


44.12 


79.20 


44.81 


79.01 


46.16 


92 


80.46 


44.60 


80.27 


44.95 


80.07 


45.30 


79.87 


45.65 


92 


93 


81.34 


45.09 


81.14 


45.44 


80.94 


45.80 


80.74 


46.15 


93 


94 


82.21 


45.57 


82.01 


45.93 


81.81 


46.29 


81.61 


46.64 


94 


95 


83.09 


46.06 


82.89 


46.42 


82.68 


46.78 


82.48 


47.14 


95 


96 


83.96 


46.54 


83.76 


45.91 


83.55 


47.27 


83.35 


47.64 


96 


97 


84.84 


147.03 


84.63 


47.40 


84.42 


47.77 


84.22 


4S.13 


97 


98 


85.71 


47.51 


85.50 


47.88 


85.29 


48.26 


86.08 


48.63 


98 


99 


86.59 


48.00 


86.38 


48.37 


86.17 


48.76 


85.95 


49.13 


99 


100 

l1 


87.46 


48.48 


87.25 


48.86 
Lat. 


87.04 


1 49.24 


86.82 


49.62 
Lat. 


100 

1 


Dep. 


Lat. 


Dep. 


Dep. 


Lat. 


Dep. 


61 


Deg. 


601 Deg. 


601 Deg. 


60J Deg. 



23 



132 



TRAVERSE TABLE. 



1, 

1 


30 Deg. 


30i Deg. 


30^ 


Deg. 


301 Deg. 


rs 

T 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.87 


0..50 


0.83 


0.50 


0.86 


0.51 


0.86 


o.sf 


2 


1.73 


1.00 


1.73 


1.01 


1.72 


1.02 


1.72 


1.02 


2 


3 


2.00 


1.50 


2 59 


1.51 


2.58 


1.52, 


2 58 


1.53 


3 


4 


3.40 


2.00 


3.46 


2.02 


3.45 


2.03 


3 44 


2.05 


4 


5 


4.33 


2.50 


4.32 


2.52 


4.31 


2.54 


4 30 


2.56 


5 


6 


5.20 


3.00 


5.18 


3.02 I 


5.17 


3.051 


5.16 


3.07 


6 


7 


6.06 


3.50 


6.05 


3.53 


6.03 


3.55 


6.02 


3.58 


1 


8 


6.93 


4.00 


6.91 


4.03 


6.89 


4.06 


6.88 


4.09 


8 


9 


7.79 


4.50 


7.77 


4.53 


7.75 


4.57] 


7.73 


4.60 


9 


10 

11 


8.66 


5.00 


8.64 
9.50 


5.04! 
5.54 


8.62 


5.08 1 


8.59 


5.11 


.0 

:1 


9.53 


5.50 


9.48 


5.58 


9.45 


5.62 


12 


10.39 


6.00 


10.37 


6.05 


10.34 


6.09 


10.31 


6.14 


12 


13 


11.26 


6.50 


11.23 


6.55 


11.20 


6.60 


11.17 


6.65 


13 


14 


12.12 


7.00 


12.09 


7.05 


12.06 


7.11 


12.03 


7.16 


14 


15 


12.99 


7.50 


12.96 


7.56 


12.92 


7.61 


12.89 


7.67 


15 


16 


13.86 


8.00 


13.82 


8.06 


13.79 


8.12 


13.75 


8. IS 


16 


17 


14.72 


8.50 


14.69 


8.56 


14.65 


8.63 


14.61 


8.69 


17 


18 


15.59 


9.00 


15.55 


9.07 


15.51 


9.14 


15.47 


9.20 


18 


19 


16.45 


9.50 


16.41 


9.57 


16.37 


9.64 


16.33 


9.71 


19 


20 
21 


17.32 


10.00 


17.28 


10.08 


17.23 


10.15 


17.19 


10.23 


20 
21 


18.19 


10.50 


18.14 


10.58 


18.09 


10.66 


18.05 


10.74 


22 


19.05 


11.00 


19.00 


11.08 


18.96 


11.17i 


18.91 


11.25 


22 


23 


19.92 


11.50 


19.87 


11.59 


19.82 


11.67 


19.77 


11.76 


23 


24 


20.78 


12.00 


20.73 


12.09 


20.68 


12.18 


20.63 


12.27 


24 


25 


21.65 


12.50 


21.60 


12.59 


21.54 


12.69 


21.49 


12.78 


25 


26 


22.52 


13.00 


22.46 


13.10 


22.40 


13.20 


22.34 


13.29 


26 


27 


23.38 


13.50 


23.32 


13.60 


23.26 


13.70 


23.20 


13.80 


27 


28 


24.25 


14.00 


24.19 


14.11 


24.13 


14.21 


24.06 


14.32 


28 


29 


25.11 


14.50 


25.05 


14.61 


24.99 


14.72 


24.92 


14.83 


29 


30 
31 


25.98 


15.00 


25.92 


15.11 


25.85 


15.23 


25.78 


15.34 


30 
31 


26.85 


15.50 


26.78 


15.62 


26.71 


15.73 


26.64 


15.85 


32 


27.71 


16.00 


27.64 


16.12 


27.57 


16.24 


27.50 


16.36 


32 


33 


28.58 


16.50 


28.51 


16.62 


28.43 


16.75 


28.36 


16.87 


33 


34 


29.44 


17.00 


29.37 


17.13 


29.30 


17.26 


29.22 


17.38 


34 


35 


30.31 


17.50 


30.23 


17.63 


30.16 


17.76 


30.08 


17.90 


35 


36 


31.18 


18.00 


31.10 


18.14 


31.02 


18.27 


30.94 


18.41 


36 


37 


32.04 


18.50 


31.96 


18.64 


31.88 


18.78 


31.80 


18.92 


37 


38 


32.91 


19.00 


32.83 


19.14 


.32.74 


19.29 


.32.66 


19.43 


38 


39 


33.77 


19.50 


33.69 


19.65 


33.60 


19.79 


33.52 


19.94 


39 


40 
41 


34.64 


20.00 


34.55 


20.15 


34.47 
35.33 


20.30 


34.38 


20.45 


40 
41 


35.51 


20.50 


35.42 


20.65 


20.81 


35.24 


20.96 


42 


36.37 


21.00 


36.28 


21.16 


36.19 


21.32 


36.10 


21.47 


42 


43 


37.24 


21.50 


37.14 


21.66 


37.05 


21.82 


36.95 


21.99 


43 


44 


38.11 


22.00 


38.01 


22.17 


37.91 


22.33 


37.81 


22.. 50 


44 


45 


38.97 


22.50 


38.87 


22.67 


38.77 


22.84 


38.67 


23.01 


45 


46 


39.84 


23.00 


39.74 


23.17 


39.63 


23.35 


39.53 


23.52 


46 


47 


40.70 


23.50 


40.60 


23.68 


40.50 


23.85 


40.39 


24.03 


i"? 


48 


41.57 


24.00 


41.46 


24.18 


41.36 


24.36 


41.25 


24.54 


48 


49 


42.44 


24.50 


42.33 


24.68 


42.22 


24.87 


42.11 


25.05 


49 


60 

g 


43.30 


25.00 


43.19 


25.19 


43.08 


25.38 


42.97 


25.56 


50 


Dep. 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 
o 

c 

2 


GO] 


Dcg. 


691 


Deg. 


59 1 


Deg. 


59i Deg. 



TRAVERSE TABLE. 



133 



c 

p 

51 


30 Deg, 


30i Deg. 


30i Dc^. 


301 Dog. 


C 

B 
n 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


44.17 


25.50 


44. p6 


25.69 


43.94 


25.88 


43.83 


26.08 


52 


45.03 


26.00 


44.92 


26.20 


44.80 


26.39 


44.69 


26.59 


52 


53 


45.90 


26.50 


45.78 


26.70 


45.67 


26.90 


45.55 


27.10 


63 


54 


46.77 


27.00 


46.65 


27.20 


46.53 


27.41 


46.41 


27.61 


54 


55 


47.63 


27.50 


47.51 


27.71 


47.39 


27.91 


47.27 


28.12 


5.T 


56 


48.50 


28.00 


48.37 


28.21 


48.25 


28.42 


48.13 


28.63 


56 


57 


49.36 


28.50 


49.24 


28.72 


49.11 


28 93 


48.99 


29.14 


67 


68 


50 23 


29.00 


50.10 


29.22 


49.97 


29.44 


49.85 


29.65 


58 


59 


51.10 


29.50 


50.97 


29.72 


50.84 


29.94 


50.70 


30.17 


59 


60 
61 


51.96 


30.00 


51.83 
52.69 


30.23 


51.70 


30.45 


51.56 


30.68 


60 

61 


52.83 


30.50 


30.73 


52.56 


30.96 


52.42 


31.19 


62 


63.69 


31.00 


53.56 


31.23 


53.42 


31.47 


53.28 


31.70 


62 


63 


54.56 


31.50 


54.42 


31.74 


54.28 


31.97 


54.14 


32.21 


63 


64 


55.43 


32.00 


55.29 


,32.24 


55.14 


32.48 


55.00 


32.72 


04 


65 


56.29 


32.50 


56.15 


32.75 


56.01 


32.99 


55.86 


33.23 


65 


66 


57.16 


33.00 


57.01 


33.25 


,56.87 


33.50 


.56.72 


33.75 


66 


67 


58.02 


33.50 


57.88 


33.75 


57.73 


34.01 


57.58 


34.26 


67 


68 


58.89 


34.00 


58.74 


34.26 


58.59 


34.51 


.58.44 


34.77 


68 


69 


59.76 


34.50 


59.60 


34.76 


59.45 


35.02 


59.30 


35.28 


69 


70 

71 


60.62 


35.00 


60.47 


35.26 


60.31 


35.53 


60.16 


35.79 


70 

71 


61.49 


35.. 50 


61.33 


35.77 


61.18 


36.04 


61.02 


36.30 


72 


62.35 


36.00 


62.20 


36.27 


62,04 


36.54 


61.88 


36.81 


72 


73 


63.22 


36.50 


63.06 


36.78 


62.90 


37.05 


62.74 


37.32 


73 


74 


64.09 


37.00 


63.92 


37.28 


63.76 


37.56 


63.60 


37.84 


74 


75 


64.95 


37.50 


64.79 


37.78 


64.62 


38.07 


64.46 


38.35 


75 


76 


65.82 


38.00 


65.65 


38.29 


65.48 


38.57 


65.31 


38.86 


76 


77 


66.68 


38.50 


66.52 


38.79 


66.35 


39.08 


66.17 


39.37 


77 


78 


67.55 


39.00 


67.38 


39.29 


67.21 


39.59 


67.03 


39.88 


78 


79 


68.42 


39.50 


68.24 


39.80 


68.07 


40.10 


67.89 


40.39 


79 


80 

81 


69.28 


40.00 


69.11 


40.30 


68.93 


40.60 


68.75 


40.90 


80 
81 


70.15 


40.50 


69.97 


40.81 


69.79 


41.11 


69.61 


41.41 


82 


71.01 


41.00 


70.83 


41.31 


70.65 


41.62 


70.47 


41.93 


82 


83 


71.88 


41.50 


71,70 


41.81 


71.52 


42.13 


71.33 


42.44 


83 


84 


72.75 


42.00 


72.56 


42.32 


72.38 


42.63 


72.19 


42.95 


84 


85 


73.61 


42.50 


73.43 


42.82 


73.24 


43.14 


73.05 


43.46 


85 


86 


74.48 


43.00 


74.29 


43.32 


74.10 


43.65 


73.91 


43.97 


86 


87 


75.34 


43.50 


75,15 


43.83 


74.96 


44.16 


74.77 


44.48 


87 


88 


76.21 


44.00 


76.02 


44.33 


75.82 


44.66 


75.63 


44.99 


88 


89 


77.08 


44.50 


76.88 


44.84 


76.68 


45.17 


76.49 


45.51 


89 


90 
91 


77.94 


45.00 


77.75 


45.34 


77.55 


45.68 


77.35 


46.02 


90 
91 


78.81 


45.50 


78.61 


45.84 


78.41 


46.19 


78.21 


46.53 


92 


79.67 


46.00 


79.47 


46.35 


79.27 


46.69 


79.07 


47.04 


92 


93 


80.54 


46.50 


80.34 


46.85 


80.13 


47.20 


79.92 


47.55 


93 


94 


81.41 


47.00 


81.20 


47.35 


80.99 


47.71 


80.78 


48.06 


94 


95 


82.27 


47.50 


82.06 


47.86 


81.85 


48.22 


81.64 


48.57 


95 


96 


83.14 


48.00 


82.93 


48.36 


82.72 


48.72 


82.50 


49.08 


96 


97 


84.00 


48., 50 


83.79 


48.87 


83.58 


49.23 


83.36 


49.60 


97 


98 


84.87 


49.00 


84.66 


49.37 


84.44 


49.74 


84.22 


60.11 


98 


99 


85.74 


49. 5i) 


85.52 


49.87 


85.30 


60.25 


85.08 


50.62 


99 


100 

§ 

e 

s 

.2 


86.60 
Dep. 


50.00 


86.38 


50.38 j 


86.16 


50.75 


85.94 


51.13 
Lat. 


100 

d 

V 

c 
O 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


60 Dog. 


591 Deg. 


69i Deg. 


594 Deg. 



134: 



TRAVERSE TABLE 



P. 


31 Deg. 


3U Dog. 


3U Deg. 


311 Deg. a 


i 


I 










.2 


Lat. 
"07S6' 


Dep. 


Lat. 

0.85 


Dep. 


Lat. 1 Dep. 


Lat. 


Dep. 


0.51 


0752" 


0.85 


0.52 


0.85 


0..53 


1 


fi : 1.71 


1.03 


1.71 


1.04 


1.71 


1.04 


1.70 


1.05 


2 


3 1 2.57 


1.55 


2.56 


1.56 


2.56 


1.57 


2.55 


1.58 


3 


4, 3.43 


2.06 


3.42 


2.08 


3.41 


2.09 


3.40 


2.10 


4 


5 4.29 


2.58 


4.27 


2.59 


4.26 


2.61 


4.25 


2.63 


5 


e . 6.14 


3.09 


5.13 


3.11 


5.12 


3.13 


5.10 


3.16 


6 


7 


6.00 


3.61 


5.98 


3.63 


5.97 


3.66 


5.95 


3.68 


7 


8 


6.86 


4.12 


6.84 


4.15 


6.82 


4.18 


6.80 


4.21 


8 


9 


7.71 


4.64 


7.09 


4.67 


7.67 4.70 1 


7.65 


4.74 


9 


10 


8.57 


5.15 


8.55 


5.19 


8. .53 I 5.22 


8.50 


5.26 


10 


11 


9 43 


5.67 


9.40 


5.71 


9.38 


5.75] 


9.35 


5.79 


11 


12 


10.29 


6.18 


10.26 


6.23 


10.23 


6.27 


10.20 


6.31 


12 


13 


11.14 


6.70 


11.11 


6.74 


11.08 


6.79 


11.05 


6.84 


13 


14 


12.00 ! 7.21 1 


11.97 


7.26 


11.94 


7.31 


11.90 


7.37 14 


15 


12.86 


7.73 


12.82 


7.78 


12.79 


7.84 


12.76 


7.89 1 15 


16 


13.71 


8.24 


13.68 


8.30 


13.64 


8.36 


13.61 


8.42' 16 


17 


14.57 


8.76 


14.53 


8.82 


14.49 1 8.83 


14.46 


8.95 


17 


18 


15.43 


9.27 


15.39 


9.34 


15.35 1 9.40 


15.31 


9.47 


18 


19 


16.29 


9.79 


16.24 


9.86 


16.20} 9.93 


16.16 


10.00 


19 


20 

21 


17.14 


10.30 


17.10 


10.38 


17.05 


10.45 


17.01 


10.52 


20 


18.00 


10.8:', 1 


17.95 


10.80 


17.91 


10.97 


17.86 


11.05 


21 


22 


18.86 


11.33 


18.81 


11.41 


18.76 


11.49 


18.71 


11.58 


22 


23 


19.71 


11.85 


19.66 


11.93 


19.61 


12.02 


19.56 


12.10 


23 


24 


20.57 


12.36 


20.52 


12.45 


20.46 


12.54 


20.41 


12.63 


24 


25 


21.43 


12.88 


21.37 


12.97 


21.32 


13.06 


'21.2.6 


13.16 


25 


26 


22.29 


13.39 


22.23 


13.49 


22.17 


13.53 


i22.ll 


13.68 


26 


27 


23.14 


13.91 


23.08 


14.01 


23.02 ' 14.11 


22.96 


14.21 


27 


28 


24.00 


14.42 


23.94 


14.53 


23.87 i 14.63 


23.81 


14.73 


28 


29 


24.86 


14.94 


24.79 


15.04 


24.73 


15.15 


,24.66 


15.26 


29 


30 
31 


25.71 


15.45 


25.65 


15.50 


25.58 
^6.43 


15.67 
16.20 


125.51 
126.36 


15.79 


30 


26.57 


15.97 


26.5a 


16.08 


16.31 


31 


32 


27.43 1 16.48 


27.36 


16.60 


27.28 


16.72 


•27.21 


16.84 


32 


33 


28.29 


17.00 


28.21 


17.12 


28.14 


17.24 


! 28.06 


17.37 


33 


34 


29.14 


17.51 


29.07 


17.64 


28.99 


17.76 


128.91 


17.89 


34 


35 


30.00 


18.03 


29.92 


18.16 


29.84 


18.29 


29.76 


18.42 


35 


36 


30.86 


18. .54 


30.78 


L8:.68 


30.70 


18.81 


30.61 


18.94 


36 


37 


31.72 


19.06 


31.63 


19.19 


31.55 


19.33 


31.46 


19.47 


37 


38 


32.57 


19.57 


32.49 


19.71 


32.40 


19.85 


I33..3I 


20.00 


38 


: 39 


33.43 


20.09 


33.34 


20.23 


1 33.25 


20.38 


|33.16 


20.52 


39 


40 
4l' 


34.29 


20.60 


34.20 


20.75 


34.11 


20.90 


134.01 


21 On 


40 


35.14 


21.12 


35.05 


21.27 


34.96 


21.42 


34.86 


21.57 


U 


42 


36.00 


21.63 


35.91 


21.79 


35.81 ,21.94 


35.71 


22.10; 12 I 


43 


36.86 


22.15 


36.76 


22.31 


36.66 


22.47 


.^,6.57 


22.63 


43 


44 


37.72 


22.66 


37.62 122.83 


37.52 


22.99 


37.42 


23.15 


44 


45 38.57 


23.18 


38.47 


23.. 34 


38.37 


23.51 


38.27 


23.68 


45 


46 


39.43 


23.69 


39.33 


23.86 


39.22 


24.03 


139.12 


24. SI 


46 


47 


40.29 


24.21 


40.18 


24.38 


40.07 


24.56 


'39.97 


24.73. 47 I 


48 


41.14 


24.72 


41 04 


24.90 


40.93 


25.08 


40.82 


25.26 


48 


49 42.00 


25.24 


41.89 


25.42 


41.78 


25.60 


41.67 


25.78 


49 


_50^|42.86 


25.75 


42.75 


25.94 


42.63- 


26.12 


42.52 


26.31 


60 


5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




5&Deg. 


58| Deg. 


58i Deg. 


58J 


Dpg, 



TRAVERSE TABLE 



135 



o 

3 
p 

"51 


31 Deg. 


2H Deg. 


3li Deg. 


3U Deg. 


p 


Lat. 


Dcp. 


Lat. Dep. 


Lat. Dep. 


Lat. 


Dep. 


43.72 126.27 


'43.60 26.46 


43.48 26.05' 


43.37 


26.84 


52 


44.57 126.78 


44.46 26.98 44.34 27.17 


44.22 


27.36 


52 


53 


45.43 I27.30 


45.31 i 27.49 |i 45. 19. 27.69^ 


45.07 


27.89 


5P; 


54 


46.29 :27.81 


46.17! 28.01 46.04; 23.21 


45.92 23.42 


54 


55 


47.14 123.33 


47.02 28.53 46.90 1 28.74 


46, >7 28.94 


55 


56 


48.00 '23.84 


47.83 29.05 |i 47.75 


29.26. 


47.62 (29.47 


56 


57 


43.86 29.36; 


48.73:29.57 48.60 


29.78' 


48.47 129.99 


57 


5S 


49.72 29.87, 


49.53 30.09 


49.45 


30.30 : 


49.32! 30.52 


58 


59 


50.57 30.39! 


50 44 30.61 


50.31 


30.83 


.50. 17 i 31.05 


59 


60 
61 


51.43 30.90 i 
52.29 31.42' 


51.29 31.13 


51.16 


31.35 1 


51.02 131.57 


60 
61 


52.15 31.65 ; 52.01 |31.87 


51.87 132.10 


62 


53.14 31.93 1 


53.00 32.16, 52.86 32.39 


52.72 1 32.63 


62 


63 


54.00 32.45 


53.86 32.68 1 53.72 132.92 


53.57 133.15 


63 


64 


54.86 32.96 


54.71 33.20 154.57 33.44 


54.42 133.63 


64 


G5 


55.72 33.43 


55.57 33.72 i 55.42 33.96 


55.27 '34.20 


65 


66 


56.57 33.99 


56.42 34.24 56.27 34.43 


56.12 34.73 


66 


67 


57.43 34.51 


57.23 34.76 57.13 35.01 


56.93 .35.26 


67 


63 


53.29 35.02 


53.13 35.23 57.93 35.53 


57.82 35.73 


68 


69 


59.14 35.54 


53.99 35.80 53.83 36.05 


53.67 36.31 


69 


70 
71 


60.00 36.05 
60.86 36.57 


59.84 36.31 , 59.63 ' 36.57 


59.52 36.83 
60.37 37.36 


70 
71 


60.70 36.83 60.54 i 37.10 


72 


61.72 37.03 


61.55 37.35 61 .39 | 37.6-:4 


61.23 37.89 


72 


73 


62.57 37.60 


62.41 37.87 62.24 j 33. 14 


62.08 33.41 


73 


74 


63.43 33.11 


63.26 33.89 63.10 33.66 


62.93 33.94 


74 


75 


64.29 33.63 


64.12 33.91 ; 63.95 1 39.19 


63.73 39.47 


75 


76 


65.14 39.14 


64.97 39.43 ' 64.80 i 39.71 


64.63 39.99 


76 


77 


66.00 39.66, 


65.83 39.95 , 65.65 40.23 


65.43 40.52 


77 


78 


C6.S6 40.17 i 


66.68 40.46 66.51 40.75 


66.33 41.04 


78 


79 


67.72 i 40.69 


67.54 40.93 ; 67.36 41.23 


67.13 41.57 


79 


80 


68.57 41.20 : 


68.39 41.50 ; 63.21 41.80 , 


63.03 42.10 


80 


81 


69.43 41.72 ■ 


69.25 42.02 ■.: 69.06 42.32 


63.83 1 42.62 


81 


62 


70.29 ; 42.23 i 


70.10 42.54 69.92:42.84 


69.73 43.15 


82 i 


83 


71.14,42.75 


70.96 43.06 70.77 : 43.37 


70.53 : 43.68 


83 


84 


72.00 i 43.26 


71.81 43.53 ,71.62 43.39 


71.43 144.20 


84 


85 


72.86 ! 43.78. 


72.67 44.10 72.47 44.41 


72.23 44.73 


85 


86 


73.72 44.29 


73.52 4-1.61 73.33 44.93 


73.13 45.25 


86 


87 


74.57 44.81 


74.33 45.13 74.18 : 45.46 


73.93 45.73 


87 


88 


75.43 45.32 


75.23 45.65 75.03 45.93 


74.83 46.31 


88 


89 


76.29 45.34; 


76.09 46.17 75.33 46.50 


75.63 46.83 


89 


90 
91 


77.15 46.35 


76.94 46.69 76.74 47.02 
77.80 47.21 77.59 ,47.55 


76.53 47.36 
77.33 ; 47.89 


90 
'91 


78.00 46.87 


92 


78.86:47.33 : 


78.65 47.73 i: 78.44 


43.07 


73.23 43.41 


92 


93 


79.72 ! 47.90 1 


79.51 48.25 179.30 


48.59 


79.03 43.94 


93 


94 


80.57 '43.41 i 


80.36 43.76 80.15 


49.11 


79.93 49.47 


94 


U5 


81.43 48.93 1 


81.22 49.23 81.00 


49.64 


80.78 <i9.99 


95 


96 


82.29 49.44 


82.07 49.80 81.85 


50.16 


81.63 i 50.52 


96 


97 


83.15 49.96 


82.93 50.32 -82.71 


50 .68 


82.48 51.04 


97 


93 


84.00 50.47 


83.78 50.34 83.56 1 51.20 


83.33 51.57 


93 


99 


84.86 50.99 


,84.64 51.36 84.41 : 51.73 


84.18 52.10 


9& 


100 

5 


85.72 51.50 
Dep. Lat. 

■ 


185.49,51.83 85.26.52.25 


85.04 ,52.62 


1^ 
c 

c 


1 Dep. 


Lat. 


Dep. 


ILat. 


Dep. Lat. 


59 De?. 


38| Deg. 


58^ Deg. 


58i Deg. 

1 



136 



TRAVERSE TABLE. 



5 

o 

o 

"T 


32 Deg. 


32i Deg. 


32^ Deg. 


32J Deg. 


P 

1 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 
0.54 


85 


0.53 


0.85 


0.53 


0.84 


0.54 


0,84 


2 


1.70 


1.06 


1.69' 1.07 


1.69 


1.07 


1.68 


1 08 


2 


3 


2.54 


1.59 


2.54 


1.60 


2.53 


1.61 


2.52 


1.62 


3 


4 


3.39 


2.12 


3.38 


2.13 


3.37 


2.15 


3.36 


2.16 


4 


5 


4.24 


2.65 


4.23 


2.67 


4.22 


2.69 


4.21 


2.70 


5 


6 


5.09 


3.18 


5.07 


3.20 


5.06 


3.22 


5.05 


3.25 


6 


7 


5.94 


3.71 


5.92 


3.74 


5.90 


3.76 


5.89 


3.79 


7 


8 


6.78 


4.24 


6.77 


4.27 


6.75 


4.30 


6.73 


4.33 


8 


9 


7.63 


4.77 


7.61 


4.80 


7.59 


4.84 


7.57 


4.87 


9 


10 

'll 


8.48 


5.30 


8.46 
9.30 


6.34 

5.87 


8.43 


5.37 


8.41 


5.41 


10 
11 


9.33 


5.83 


9.28 


5.91 


9.25 


5.95 


12 


10.18 


6.36 


10.15 


6.40 


10.12 


6.45 


10.09 


6.49 


12 


13 


11.02 


6.89 


10.99 


6.94 


10.96 


3.98 


10.93 


7.03 


13 


14 


11.87 


7.42 


11.84 


7.47 


11.81 


7.52 


11. -77 


7.57 


14 


15 


12.72 


7.95 


12.69 


8.00 


12.65 


8.06 


12.62 


8.11 


15 


16 


13.57 


8.48 


13.53 


8.54 


13.49 


8.60 


13.46 


8.66 


16 


17 


14.42 


9.01 


14.38 


9.07 


14.. 34 


9.13 


14.30 


9.20 


17 


18 


15.26 


9.54 


15.22 


9.61 


15.18 


9.67 


15.14 


9.74 


18 


19 


16.11 


10.07 


16.07 


10.14 


16.02 


10.21 


15.98 


10.28 


19 


20 


16.% 


10.60 


16.91 


10.67 
11.21 


16.87 


10.75 


16.82 


10.82 


20 

21 


21 


17. «1 


11.13 


17.76 


17.71 


11.28 


17.66 


11. .36 


22 


18.66 


11.06 


18.61 


11.74 


18.. 55 


11.82 


18.50 


11.90 


22 


23 


19.51 


12.19 


19.45 


12.27 


19.40 


12.36 


19.34 


12.44 


23 


24 


20.35 


12.72 


20.30 


12.81 


20.24 


12.90 


20.18 


12.98 


24 


25 


21.20 


13.25 


21.14 


13.34 


21.08 


13.43 


21.03 


13.52 


25 


26 


22.05 


13.78 


21.99 


13.87 


21.93 


13.9.7 


21.87 


14.07 


26 


27 


22.90 


14.31 


22.83 


14.41 


22.77 


14.51 


22.71 


14.61 


27 


28 


23.75 


14.84 


23.68 


14.94 


23.61 


15.04 


23.55 


15.15 


28 


29 


24.59 


15.37 


24.. 53 


15.47 


24.46 


15.58 


24.39 


15.69 


29 


30 
31 


25.44 


15.90 


25.37 


16.01 


25.30 
26.15 


16.12 


25.23 


16.23 


30 


26.29 


16.43 


26.22 


16.54 


16. G6 


26.07 


16.77 


31 


32 


27.14 


16.96 


27.06 


17.08 


26.99 


17.19 


26.91 


17.31 


32 


33 


27.99 


17.49 


27.91 


17.61 


27.83 


17.73 


27.75 


17.85 


33 


34 


28.83 


18.02 


28.75 


18.14 


28.68 


18.27 


28.60 


18.39 


34 


35 '29.68 


18.55 


29.60 


18.68 


29.52 


18.81 


29.44 


18.93 


35 


36 30.53 


19.08 


30.45 


19.21 


30.36 


19.34 


30.28 


19.48 


36 


.37 31.38 


19.61 


31.29 


19.74 


31.21 


19.88 


31.12 


20.02 


37 


38 32.23 


20.14 


32.14 


20.28 


32.05 


20.42 


31.96 


20.56 


38 


39 33.07 


20.67 


32.98 


20.81 


32.89 


20.95 


32.80 


21.10 


39 


40 


33.92 


21.20 


33.83 


21.34 


33.74 


21.49 


33.64 


21.64 


40 


41 


34.77 21.73 1 


34.67 


21.88 


34.58 


22.03 


34.48 


22.18 


41 


42 


35.62 


22.26 


35.52 


22.41 


35.42 


22.57 


35.32 


22.72 


42 


43 


36.47 


22.79 


36.37 


22.95 


36.27 


23.10 


36.16 


23.26 


43 


44 


37.31 


23.32 


37.21 


23.48 


37.11 


23.64 


37.01 


23.80 


44 


45 


38.16 


23.85 


38.06 


24.01 


37.95 


24.18 


37.85 


24.34 


45 


46 


39.01 


24.38 


38.90 


24.55 


38.80 


24.72 


38.69 


24.88 


46 


47 


30.86 


24.91 


39.75 


25.08 


39.64 


25.25 


39.53 


25.43 


47 


48 


40.71 


25.44 


40.59 


25.61 


40.48 


25.79 


40.37 


25.97 


4S 


49 


41.55 


25.97 


41.44 


26.15 


41.33 


26.33 


41.21 


26.51 


49 


50^ 


42.40 


26.50 


42.29 


26.68 


42.17 26.86 


42.05 


27.05 


50 

c 
Q 





Dep. 


Lat. 


Dep. Lat. 


Dep. 1 Lat. 


Dep. 


Lat. 


58 Deg. 


571 Deg. 


57i Deg. 


57U 


Deg. 



TRAVERSE TABLE. 



137 



t 

51 


32 Deg. 


32i Deg. 


1 
32i Deg. 


321 Deg. 


'^1 


Lat. 
43.25 


Dep. 


Lat. 


Dep. 


Lat. 
43.01 


Dep. 

"27.40: 


Lat. 


Dep. 


27.03 


43.13 


27.21 


42.89 


27.59 


52 


44.10 27.56 il 43.98 


27.75 


43.86 


27.94' 


43».73 


28.13 


52 


53 


4^1.95 28.09 il 44. 82 


28.28 


44.70 


28.48 


44.58 


28.67 


53 


54 


45.79 128.62 45.67 
46.64 129.15 146.51 


28.82 145.54 


29.01 j 


45.42 


29.21 


54 


55 


29,35 i! 46.39 


29.55 1 


46.26 


29.75 


55 


66 


47.49 129.68 47.36 


29.88 ;| 47.23 


30.09 i 


47.10 


30.29 


56 


57 


48.84 '30.21 ! 48.21 


30.42 148.07 


30.63! 


47.94 


30.84 


57 


58 49.19 ,30.74! 49.05 


30.95! 


48.92 


31.16 


48.78 


31.38 


58 


59 50.03 


31 27 149.90 


31.48 


49.76 


31.70| 


49.62 


31.92 


69 


60 


50.88 


31.80 150.74 


32.02. 


50.60 


32.24 


50.46 


32.46 
33.00 


60 
61 


61 


51.73 


32.33 1151.59 


32.55 ii 51.45 


32.78 51.30 


62 


52.58 


32.85 52.44 


33.08 ': 


52.29 


33.311 


52.14 


33.54 


62 


63 


53.43 


33.38 153.28 


33.62! 


53.13 


33.85 1 


52.99 


34.08 


63 


64 


54.28 


33.91 54.13 


34.15 


53.98 


34.39 1 


53.83 


34.62 


64 


65 


55.12 


34.44 


54.97 


34.68 


54.82 


34.92 


54.67 


35.16 


65 


60 


55.97 


34.97 1 


55.82 


35.22 


55.66 


35.40 


55.51 


35.70 


68 


67 


56.82 


35.50 ! 


56.66 


35.75 


56.51 


30.00! 


56.35 


36.25 


67 


68 


57.67 


36.03! 


57.51 


36.29 


57.35 


36.541 


57.19 


36.79 


68 


69 


58.52 


36.56 


58.36 


36.82 


58.19 


37.07 


.58.03 


37.33 


69 


70 
71 


59.36 


37.09 


59.20 


37.35 


59.04 
59.88 


37.61 
38.15 


58.87 


37.87 


70 
71 


60.21 


37.62: 


60.05 


37.89 


59.71 


38.41 


72 


61.06 


38.15 1 60.89 1 38.42 


60.72 


38.69! 


60.55 


38.95 


72 


73 


61.91 


38.68 61.74 
39.21 62.58 


38.95 


61.57 


39 . 22 i 


61.40 


39.49 


73 


74 


62.76 


39.49 


62.41 


39.-/6 


62.24 


40.03 


74 


75 


63.60 


39.741 


63.43 


40.02 


63.25 


40.30 


63.08 


40.57 


75 


76 


64.45 


40.27 


64.28 


40.55 


64.10 


40.83 


63.92 


41.11 


76 


77 


65.30 


40.80 


65.12 


41.09 


64.94 


41.37 


64.76 


41.65 


77 


78 


66.15 


41.33 


65.97 


41.62 


65.78 


41.91 


65.60 


42.20 


78 


79 


67.00 


41.86 1 


66.81 


42.16 


66.63 


42 45 


66.44 


42.74 


79 


80 
81 


67.84 
68.69 


42.39 i 

42.92 


67.66 
68.50 


42.69 


67.47 142.98 


67.28 


43.28 
43.82 


80 
81 


43.22 


,68.31 1 43.52 


68.12 


82 


69.54 


43.45 1 


69.35 


43.76 


69.16 144.06 


68.97 


44.36 


82 


83 


70.39 


43.98! 


70.20 


44.29 


70.00 [44.60 


69.81 


44.90 


83 


84 


71.24 


44.51] 


71.04 


44.82 


170.84 45.13 


70.65 


45.44 


84 


85 


72.08 


45.04 


71.89 


45.36 


171.69 45.67 


171.49 


45.98 


85 


86 


72.93 


45.57 


72.73 


45.89 


172.53 46.21 


72.33 


46.52 


86 


87 


73.78 


46.10 


73.. 58 


46.42 


73.38 146.75 


73.17 


47.06 


87 


88 


74.63 


46.63 


74.42 


46.96 


i 74.22 147.28 


74.01 


47.61 


88 


89 


75.48 '47. 16 


75.27 


47.49 


75.06 147.82 


74.85 


48.15 


89 


90 
91 


76.32 47.69 


76.12 
76.96 


48.03 


75.91 48.36 


75.09 


48.69 


90 


77.17 


148.22 


48.56 


76.75 48.89 


176.53 


49.23 


91 


92 


78.02 


48.75 


77.81 


49.09 


77.59 49.43 


177.38 149 77 


92 


93 


78.87 


49.28 


78.65 


1 49.63 


178.44 49.97 


1 78.22 


50.31 


93 


94 


79.72 


49.81 


79.50: 50.16 


79.28 50.51 


179.06 


50.85 


94 


95 


80.56 150.34 


i 80.34; .50.69 


!80.12 -51.04 


79.90 


51.39 


95 


96 


81.41 {50.87 


81.19 ! 51.23 


80. 97 151. 58 


80.74 


51.93 


96 


97 


82.26 51.40 


82.04 


51.76 


181.81 ;52.12 


! 81.58 


,52.47 


97 


98 


83.11 '51.93 


82.88 


52.29 


182.65 


52.66 


i 82.42 


5.'^.02 


98 


99 


83.96 52.46 


83.73 


52.83 il 83.50 


53.19 


183.26 1.53.56 


99 


100 

1 

es 


84.80 1 52.99 


84.57! 53.36 
Dep. Lat. 


1 84.34 


53.73 


J84.10 
1 Dep. 


154.10 


100 


Dep. 


Lat. 


Dep. 


Lat, 


1 Lat. 




i 58 Deg. 


1 
571 Deg. 57i Deg. 


1 

57i Deg. 

1 


3 



138 



TRAVERSE TABl E. 



o 
1 


33 Deg. 


m Deg. 


33i Deg 


331 Deg. 


O 

3 
O 

n 

T 


Lat. 


Dep. 


Lat. 

0.84 


Dep. 


Lat. 


Dep. 


Lat. 

i).83 


Dep. 
~0T66 


0.84 


0.54 


0.55 


0.83 


0.55 


2 


1.68 


1.09 


1.67 


1. 10 


1.67 


1.10 


1.66 


1.11 


2 


a 


2.52 


1.63 


2.51 


1.64 


2.50 


1.06 


2.49 


1 67 


3 


4 


3.35 


2.18 


3.S5 


2.19 


3.34 


2.21 


3.33 


2.22 


4 


6, 4.19 


2 72 


4.18 


2.74 


4.17 


2.76 


4.16 


2.78 


5 


6 5.03 


3 27 


5.02 


3.29 


5.00 


3.31 


4.99 


3.33 


fi 


7! 5.87 


3 81 


5.85 


3.84 


5.84 


3.86 


5.82 


3.89 


7 


8 1 6.71 


4.36 


6.69 


4.39 


6.67 


4.42 


6.65 


4.44 


8 


9 


7.55 


4.90 


7.53 


4.93 


7.50 


4.97 


7.48 


5.00 


9 


10 

11 


8.39 
9.23 


6.45 
5.99 


8.36 
9.20 


5.48 
6.03 


8.34 
9.17 


5.52 


8.31 


5.56 


10 


6.07 


9.15 


6.11 


11 


12 


10.06 


6.54 


10.04 


6.58 


10.01 


6.62 


9.98 


6.67 


12 


13 


10.90 


7.08 


10.87 


7.13 


10.84 


7.18 


10.81 


7.22 


13 


14 


11.74 


7.62 


11.71 


7.68 


11.67 


7.73 


11.64 


7.78 


14 


1.5 


12.58 


8.17 


12.54 


8.22 


12.51 


8.28 


12.47 


8.33 


15 


16 


13.42 


8.71 


13.38 


8.77 


13.34 


8.83 


13.30 


8.89 


16 


17 


14.26 


9.26 


14.22 


9.32 


14.18 


9.38 


14.13 


9.44 


17 


18 


15.10 


9.80 


15.05 


9.87 


15.01 


9.93 


14.97 


10.00 


18 


19 


15.93 


10.35 


15.89 


10.42 


15.84 


10.49 


15.80 


10. 5G 


19 


20 


16.77 


10.89 


16.73 


10.97 


16.68 


11.04 


16.63 


ll.il 


20 
21 


21 


17.61 


11.44 


17.56 


11.51 


17.51 


11.59 


17.46 


11.67 


22 


18.45 


11.98 


18.40 


12.06 


18.35 


12.14 


18.29 


12.22 


22 


23 


19.29 


12.53 


19.23 


12.61 


19.18 


12.69 


19.12 


12.78 


23 


24 


20.13 


13.07 


20.07 


13.16 


20.01 


13.25 


19.96 


13.33 


24 


25 


20.97 


13.62 


20.91 


13.71 


20.85 


13.80 


20.79 


13.89 


25 


26 


21.81 


14.16 


21.74 


14.26 


21.68 


14.35 


21.62 


14.44 


26 


27 


22.64 


14.71 


22.58 


14.80 


22.51 


14.90 


22.45 


15.00 


27 


28 


23.48 


15.25 


23.42 


15.35 


23.35 


15.45 


23.28 


15.56 


28 


29 


24.32 


15.79 


24.25 


15.90 


24.18 


16.01 


24.11 


16.11 


29 


30 
31 


25.16 


16.34 


25.09 


16.45 
17.00 


25.02 


16.56 


24.94 


16.67 


30 
31 


26.00 


16.88 


25.92 


25.85 


17.11 


25.78 


17.22 


32 


26.84 


17.43 


26.76 


17.55 


26.68 


17.66 


26.61 


17.78 


32 


33 


27.68 


17.97 


27.60 


18.09 


27.52 


18.21 


27.44 


18.33 


33 


34 


28.51 


18.52 


28.43 


18.64 


28.35 


18.77 


28.27 


13.89 


34 


3.^^ 


29.35 


19.06 


29.27 


19.19 


29.19 


19.32 


29.10 


19.44 


35 


36 


30.19 


19.61 


30.11 


19.74 


30.02 


19.87 


29.93 


20.00 


36 


37 


31.03 


20.15 


30.94 


20.29 


30.85 


20.42 


30.76 


20.. 56 


37 


38 


31.87 


20.70 


31.78 


20.84 


31.69 


20.97 


31.60 


21.11 


38 


39 


.32,71 


21.24 


32.62 


21.38 


32.52 


21.53 


32.43 


21.67 


39 


40 
41 


33.55 


21.79 


33.45 
34.29 


21.93 


33.36 
34.19 


22.08 
22.63 


33.26 


22.22 


40 
41 


34.39 


22.33 


22.48 


34.09 


22.78 


A9, 


35.22 


22.87 


35.12 


23.03 


35.02 


23.18 


34.92 


23.33 


«-2 


43 


36.00 


23.42 


35.96 


23.58 


35.86 


23.73 


35.75 


23.89 


43 


44 


36.90 


23.96 


36.80 


24.12 


36.69 


24.29 


36.58 


24.45 


44 


45 


37.74 


24.51 


37.63 


24.67 


37.52 


24.84 


37.42 


25 00 


45 


46 


38.58 


25.05 


38.47 


25.22 


38.36 


25.39 


38.25 


25.53 


46 


47 


39.42 


25.60 


39.31 


25.77 


39.19 


25.94 


39.08 


26.11 


47 


48 


40.28 


26.14 


40.14 


26.32 


40.03 


26.49 


39.91 


26.67 


48 


49 


41.09 


26.69 


40.98 


26.87 


40.86 


27.04 


40.74 


27.22 


49 


50 


41.93 


27.23 


41.81 


27.41 


41.69 


27.60 


41.57 


27.78 


Uo 


oi 

a 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


57 Deg. 


56| Deg. 


56i Deg. 


£«i Deg. 


Q 



TRAVERSE TABLE. 



139 



i 

51 


33 Deg. 

I 


33i Deg. 


33^ Deg. 


33J Deg. 


1 

51 


Lat. 


Dep. 


Lat. 


Dop. 


Lat. 


Dep. 
28.15 


Lat. 


Dep. 


42.77 


27.78 


42.65 


27.96 


42.53 


42.40 


28.33 


52 


43.61 


28.32 


43.49 


28.51 


43.36 


28.70 


43.24 


28.89 


62 


53 


44.45 


28.87 


44.32 


29.06 


44.20 


2^.25 


44.07 


29.45 


63 


54 


45.29 


29.41 


45.16 


29.61 


45.03 


29.80 


44.90 


30.00 


54 


65 


46.13 


29.96 


46.00 


30.16 


45.86 


30.36 


45.73 


30.56 


55 


66 


48.97 


30.. 50 


46.83 


30.70 


46.70 


30.91 


46.56 


31.11 561 


67 


47.80 


31.04 


47.67 31.25 1 


47.53 


31.46 


47.39 


31.67 


57 


68 


48.64 


31.59 


48.50 


31.80 


48.37 


32.01 


4fi.2-3 


32.22 


58 


59 


49.48 


32.13 


49.34 


32.35 


49.20 


32.56' 


49.06 


32.78 


59 


60 
61 


50.32 


32.68 


50.18 


32.90 


50.03 

50.87 


33.12 


49.89 


33.33 


60 
61 


51.16 


33.22 


51.01 


33.45 


33.67 


50.72 


33.89 


62 


.52.00 


33.77 


51.85 


33.99 


51.70 


34.22 


51.55 


34.45 


62 


63 


52.84 


34.31 


52.69 


34.54 


52.53 


34.77 


52.38 


35.00 


63 


61 


53.67 


34.86 


53.52 


35.09 


53.37 


35.32 


53.21 


35.56 


64 


65 


54.51 


35.40 


54.36 


35.64 


54.20 


35.88 


54.05 


36.11 


65 


66 


55.35 


35.95 


55.19 


36.19 


.55.04 


36.43 


54.88 


36.67 


Gj 


67 


56.19 


36.49 


56.03 


36.74 


55.87 


36.98 


55.71 


37.22 


'67 


68 


57.03 


37.04 


56.87 


37.28 i 


56.70 


37.53 


56.54 


37.78 


68 


69 


57.87 37.58! 


57.70 


37.83 


57.54 


38.08 


57.37 138.33 


69 


70 
71 


58.71 


38.121 


58.54 


38.38 


.58.37 


38.64 


58.20 


38.89 
39.45 


70 

71 


59.55 


.38.67 


59.38 


38.93 


59.21 


39.19 


59.03 


72 


60.38 


39.21 


60.21 


39.48 


60.04 


39.74 


.59.87 40.00 


72 


73 


61.22 


39.76 


61.05 


40.03 


60.87 


40.29 


60.70 40.56 


73 


74 


62.06 


40.30 1 


61.89 


40.57 


61.71 


40.84 


61.53 


41.11 


74 


75 


62.90 


40.85 1 


62.72 


41.12 


62.. 54 


41.40 


62.36 


41.67 


75 


76 


63.74 


41.39! 


63.56 


41.67 


63.38 


41.95 


63.19 


42.22 


76 


77 


64.58 


41.94 


64.39 


42.22 


64.21 


42.50 


64.02 


42.78 


77 


78 


65.42 


42.48 


65.23 


42.77 


65.04 


43.05 


64.85 


43.33 


78 


79 


66.25 


43.03 


66.07 


43.32 


65.88 


43.60 


65.69 


43.89 


79 


80 

81 


67.09 
67.93 


43.57 


66.90 


43.86 


66.71 


44.15 


66.52 


44.45 


80 
81 


4-t.l2 


67.74 


44.41 


67.54 


44.71 


67.35 


45.00 


82 


68.77 


44.66 


68.58 


44.96 


68.38 


45.26 


68.18 


45.56 


82 


83 


69.61 


45.20 


69.41 


45.51 


69.21 


45.81 


69.01 


46.11 


83 


84 


70.45 


45.75 


70.25 


46.06 


70.05 


46.36 


69.84 


46.67 


84 


85 


71.29 


46.29 


71.08 


46.60 


70.88 


46.91 


70.67 


47.22 


85 


86 


72.13 


46.84 


71.92 


47.15 


71.71 


47.47 


71.51 


47.78 


86 


87 72.96 


47.38 


72.76 


47.70 


72.55 


48.02 


72.34 


48.33 


87 


88 73.80 


47.93 


73.59 


48.25 


73.38 


48.57 


73.17 


48.89 


88 


89 


74.64 


48.47 


74.43 


48.80 


74.22 


49.12 


74.00 


49.45 


89 


90 
91 


75.48 


49.02 


75.27 
76.10 


49.35 
49.89 


75.05 


49.67 


74.83 
75.66 


50.00 


90 


76.32 


49.56 


75.88 


50.23 


50.56 


91 


92 


77.16 


50.11 


76.94 


50.44 


76.72 


50.78 


•76.50 


51.11 


92 


93 178.00 


50.65 


77.77 


50.99 


77.55 


51.33 


77.33 


51.67 


93 


94 


78.83 


51.20 


78.61 


51.54 


78.39 


51.88 


78.16 


52.22 


94 


95 


79.67 


! 51.74 


79.45 


52.09 


79.22 


52.43 


78.99 


52.78 


95 


96 


80.51 


52.29 


80.28 


52.64 


80.05 


52.99 


; 79.82 


53.33 


96 


97 


81.35 


52.83 


81.12 


53.18 


80.89 


53.54 


•80.65 


53.89 


97 


98 


82.19 


53.37 


81.96 


53.73 


81.72 


54.09 


81.48 


54.45' 98 


99 


83.03 


153.92 


82.79 


54.28 


82.55 


54.64 


i 82.32 


55.00 99 


i 


83.87 


54.46 


83.63 


54.83 


83.39 


55.19 


83.15 


55.56, 00 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 g 


57 Deg. 


56^ Deg. 


56]- Deg. 


j 56^ 


Deg. 





140 



TRAVERSE lABLE. 





34Deg. 

1 


34i Peg. 


34^ Deg. 


34i Deg. 


i 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


'T 


0.83 


0.56 


0.83 


0.56 


T.W 


0.67 


0.82 


C.57 


1 


2 


1.66 


1.12 


1.65 1.13 


1.65 


1.13 


1.64 


.1.14 


2 


3 


2.49 


1.68 


2.48 


1.69 


2.47 


1.70 


2.46 


1.71 


3 


4 


3.32 


2.24 


3.31 


2.25 


3.30 


2.27 


3.29 


2.28 


4 


5 


4.15 


2.80 


4.13 


2.81 


4.12 


2.83 


4.11 


2.S5 


5 


6 


4.97 


3.36 


4.96 


3.38 


4.94 


3.40 


4.93 


3.42 


6 


7 


5.80 


3.91 


5.79 


3.94 


6.77 


3.9G 


6.75 


3.99 


7 


8 


6.63 


4.47 


6.61 


4.50 


6.59 


4.53 


6.57 


4.56 


8 


9 


7.46 


5.03 


7.44 


5.07 


7.42 


5.10 


7.39 


C.13 


9 


10 
11 


8.29 


5.59 


8.27 
9.09 


5.63 
6.19 


8.24 


5.66 


8.22 


5.70 
6.27 


10 
11 


9.12 


6.15 


9.07 


6.23 


9.04 


12 


9.95 


6.71 


9.92 


6.75 


9.89 


6.80 


9.86 


6.84 


12 


13 


10.78 


7.27 


10.75 


7.32 


10.71 


7.36 


10.68 


7.41 


13 


14 


11.61 


7.83 


11.57 


7.88 


11.54 


7.93 


11.50 


7.98 


14 


15 


12.44 


8.39 


12.40 


8.44 


12.36 


8.50 


12.32 


8.55 


15 


16 


13.26 


8.95 


13.23 


9.00 


13.19 


9.06 


13.15 


9.12 


16 


17 


14.09 


9.51 


14.05 


9.57 


14.01 


9.63 


13.97 


9.69 


17 


18 


14.92 


10.07 


14.88 


10.13 


14.83 


10.20 


14.79 


10.26 


18 


19 


15.75 


10.62 


15.71 


10.69 


15.66 


10.76 


15.61 


10.83 


19 


20 


16.58 


11.18 


16.53 


11.26 


16.48 


11.33 


16.43 


11.40 


20 


21 


17.41 


11.74 


17.36 


11.82 


17.31 


11.89 


17.25 


11.97 


21 


22 


18.24 


12.. 30 


18.18 


12.38 


18.13 


12.46 


18.08 


12.54 


22- 


23 


19.07 


12.86 


19.01 


12.94 


18.95 


13.03 


18.90 


13.11 


23 


24 


19.90 


13.42 


19.84 


13.51 


19.78 


13.59 


19.72 


13.68 


24 


25 


20.73 


13.98 


20.66 


14.07 


20.60 


14.16 


20.54 


14.25 


25 


26 


21.55 


14.54 


21.49 


14.63 


21.43 


14.73 


21.36 


14.82 


26 


27 


22.38 


15.10 


22.32 


15.20 


22.25 


15.29 


22.18 


15.39 


27 


28 


23.2] 


15 66 


23.14 


15.76 


23.08 


15.86 


23.01 


15.96 


28 


29 


24.04 


16.22 


23.97 


16.32 


23.90 


16.43 1 


23.83 


16.53 


29 


30 


24.87 


16.78 


24.80 


16.88 


24.72 


16.99 


24.65 
25.47 


17.10 
17.67 


30 
31 


31 


25.70 


17.33 


25.02 


17.45 


25.55 


17.56 


32 


26.53 


17.89 


26.45 


18.01 


26.37 


18.12 


26.29 


18.24 


32 


33 


27.36 


18.45 


27.28 


18.57 


27.20 


18.69 


27.11 


18.81 


33 


34 


28.19 


19.01 


28.10 


19.14 


28.02 


19.26 


27.94 


19.38 


34 


35 


29.02 


19.57 


28.93 


19.70 


28.84 


19.82 


28.76 


19.95 


35 


36 


29.85 


20.13 


29.76 


20.26 


29.67 


20.39 


29.58 


20.52 


36 


37 


30.67 


20.69 


30.58 


20.82 


30.49 


20.96 


30.40 


21.09 


.r 


38 


31.50 


21.25 


31.41 


21.39 


31.32 


21.52 


31.22 


21.66 


3>j 


39 


32.33 


21.81 


32.24 


21.95 


32.14 


22.09 


32.04 


22.23 


39 


40 


33.16 i 22.37 


33.06 


22.51 


32.97 
33.79 


22: 06 


32.87 


22.80 


40 
41 


41 


33.99 1 22.93 


33.89 


23.07 


23.22 


33.69 


23.37 


42 


34.82 


23.49 


34.72 


23 64 


34.61 


23.79 


34.51 


23.94 


4^ 


43 


35.65 


24.05 


35.54 


24 20 


35.44 


24.36 


35.33 


24.51 


43 


44 


36.48 


24.60 


36.37 


24 70 


36.26 


24.92 


36.15 


25.03 


44 


45 


37.31 


25.16 


37.20 


25 .33 


37.09 


25.49 


36.i,7 


25.65 


45 


46 


.38.14 


25.72 


38.02 


25 89 


37.91 


26.05 


37.80 126.22 


46 


47 


38.96 


26.28 


38.85 


26.45 


38.73 


26.62 


38.02 126.79 


47 


48 


39.79! 26.84 


39.68 


27.01 


39.56 


27.19 


39.44 


27.36 


48 


49 


40.62 27.40 


40.50 


27.58 


40.38 


27.75 


40.26 


27.93 


49 


50 


41.45 27.96 


41.33! 28.14 


41.21 


28.32 


41.08 


28.50 


60_ 


1 


Dep. Lat. 


Dep. Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


56 Deg. 


55J Deg. 


55^ Deg. 


5h^ Deg. 



TRAVEKSE TABUS 



141 





34Deg. 


34i Deg. 


34ADeg. 


341 Deg. 


c 

i 


Lat. i Dep. 


Lat. 


Dep. ji Lat. 

ii 


Dep. ! 


Lat. 


Dep. 


T] ! 


42.23 128.52: 42.16 


28.70 42.03 28.89 i 


41.90 29.07 


51 


62 ; 


43.11 ■ 29.08 ij 42.98 


29.27 ii 42.85 1 29.45 


42.73 29.64 


52 


63' 


43.94 29.64 1 43.81 


29.83 143.68 '■ .30.02 1 


43. .55 30.21 


53 


54 


44.77 30.20 1 44.64 


30.39 ! 44.50! 30.59 j 


44.37' 30 78 | 


54 


55 


45.60 30.76 1 45.46 


30.95:145.33 i 31.15 


45.19 


31.35 1 


55 


56 


40.43 31.31 '46.29 


31.52 '46.15 : 31.72 


46 01 


31.92 i 


56 


57 


47.26 31.87 47.12 


32.08; 46. 9S! 32 29 


46.83 


32.49 ' 


57 


58 


43.08 32.43 47.94 


32.64 Ii 47.80 132.85 


47.66 


33.00 ' 


53 


59 48.91 ; 32.99 48.77 


33.21 ! 48.62 33.4,2 


48.48 


33.63 i 


59 


60 49.74 33.55 49.60 

61 50.57,34.11:50.42 


33.77 1)49.45 33.98 


49.30 


34.20 


60 
'61 


34.33 '50.27 34.55 


50.12 


34.77 1 


62 51.40 34.67 !| 51.25 


34.89;;51.10 35.121 


50.94 


35.34 


62 


63 52.23 35.23 jl 52.03 


35.46 !j 51.92 35.68 


51.76 


35.91 


63 


64 53.06 35.79 52.90 


36.02 152.74 36.25 1 


52.59 


36.48 


64 


65 53.89 36. 35 1 53.73 


36.53 1' 53.57 36.82 i 


53.41 


37.05 i 


65 


66 54.72 36.91 ; 54.5c 


37.15 ''54.39 37.38; 


54.23! 37.62 


66 


67 


55.55 37.46 55.38 


37.71 ;l 55.22 i 37.95 i 


55.05 38.19! 


67 


08 


56.37 38.03 56.21 


38.27, 


56.04 


38.52! 


55.87 


38.76 


68 


69 


57.20 38.58 i 57.03 


38.83 


56.86 


39.08 1 


56.69 


39.33 


69 


70 
" 71 


5S.03 39. 14 {157.86 
58.86 39.70 '58.69 


39.40 j 
39.96! 


57.69 


39.65 1 

40.21 1 


57.52 


39.90 


70 
71 


58.51 


58.34 


40.47 


72 


59.69 40.26 ' 59.51 


40.52! 


59.34 


40.78 i 


59.16 


41.04 


72 


73 


60.52 40.82 160.04 


41.08 1 


60.16 41.35: 


59.98 


41.61 


73 


74 


61.35 ,41.38 ]\ 61.17 


41.65 


60.99 


41.91 i 


60.80 


42.18 


74 


75 


62.18 41. 94i| 61.99 


42.21 


61.81 


42.48 


61.62 


42.75 


75 


76 


63.01 1 42.50 1162.82 
63.84 i 43.06 II 63.65 


42.77 


62.63 


43.05 


62.45 


43.32 


76 


77 


43.34 


63.46 


43.61 


63.27 


43.89 


77 


78 


64.66 i 43.62 ii 64.47 


43.90 


64.28 


44.18 


64.09 


44.46 


. 78 


79 


65.49 [44. 18 1165.30 


44.46 


65.11 


44.75 


64.91 


45.03 


79 


80 
81 


66.32 
67.15 


44.74 


66.13 


45.02 
45.59 


65.93 


45.31 


65.73 


45.60 


80 
81 


45.29 


66.95 


66.75 


45.88 


66.55 


46.17 


82 


67.98 45.85 1 


67.78 


46.15 


67.. 58 


46.45 


67.37 46.74 


82 


83 


68.81 


46.11 


68.61 


46.71 


68.40 


47.01 


68.20 


47.31 


83 


84 


69.64 


46.97 


69.43 


47.28 


69.23 


47.58 


69.02 


47.88 


84 


85 


70.47 


47.53 1! 70.26 


47.84 


70.05 


48.14 


69.84 


48.45 


85 


86 


71.30 


48.09 l! 71.09 


48.40 


70.87 


48.71 


70.66 


49.02 


86 


87 


72.13 


48.65 1171.91 


48.96 


71.70 


49.28 


71.48 


49.59 


87 


88 


72.96 


49.21 72.74 


49.53 


72.52 


49.84 


: 72.30 


50.16 


88 


89 


73.78 


49.77 11 73.57 


50.09 


i 73.35 


50.41 


73.13^ 50 73 


89 


90 
91 


74.61 


50.33 


1 74.39 


50.65 


1 74.17 


50.98 


; 73.95, 51.30 


90 
91 


75.44 


50.89 


75.22 


51.22 


1 75.00 


51.54 


174.77 


51.87 


92 


76.27 


51.45 


76.05 


51.78 


175.82 


52.11 


175.59 


52.44 


92 


93 


77.10 1 52.00 


76.87 


52.34 


176.64 


52.68 


76.41 


53.01 


93 


94 


77.93 


52.56 


77.70 


52.90 


j 77.47 


53.24 


177.23 


53.58 


94 


95 


78.76 


53.12 


78.53 


53.47 


78.29 


53.81 


.78.06 


54.15 


l)n 


96 


79.59 


53.68 


79.35 


54.03 


179.12 


54.37 


.78.88 


54.72 


90 


97 


80.42 


54.24 


80.18 


54.59 


79.94 


54.94 


79 70 


55.29 


97 


98 


81.25 


54.80 


81.01 


55.15 


80.76 


55.51 


,80 52 


55.86 


93 


99 


82.07 


55.36 


81.83 


55.72 


81.59 


56.07 


:si..34 


56.43 


99 


100 

1 


82.90 


55.92 


82.66 


56.28 


182.41 


56.64 


1 82.16 


57.00 


100 

a 

'oa 


Dep. 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


j Dep. 


I Lat. 


56 Deg. 


551 


Deg. 


554 Deg. 


55i Deg, 



142 



TRAVERSfi TABLE. 



§ 


35 Deg. 


35i Deg. 


35i Deg. 


351 Deg. 


5 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. Dep. 


Lat. Dep. 

0.81 0.58 


1 


0.82 


0.57 


0.82 


0.58 


0.81 1 0.58 


2 


1.64 


1.15 


1.63 1.15' 


1.63 1.16 


1.62 1.17 


2 


3 


2.46 


1.72 


2.45 1 1.73. 


2.44| 1.74 


2.43 1.75 


3 


4 


3.28 


2.29 


3.27 1 2.31 1 


3.26! 2.32 


3.25 2.34 i 4 


5 


4.10 


2.87 


4.08 2.89 1 


4.07 1 2.9ff| 


4.06 2.92 1 5 


6 


4.91 


3.44 


4.90 


3.46 1 


4.83 


3.48 


4.87 


3.51, 3 


7 


5.73 


4.01 


5.72 


4.04 1 


5.70 


4.06 


5.68 


4.09 7 \ 


8 


6.55 


4.59 


6.53 


4.62 


6.51 


4.65 


6.49 


4.67 S i 


9 


7.37 


5.16 


7.35 


5.19 1 


7.33 


5.23 


7.30 


6.26 9 j 


10 


8.19 


5.74 


8.17 


5.77 1 


8.14 


5.81 


8.12 
8.93 


5.84 
6.43 


10 
11 


" 11 


9.01 


6.31 


8.93 


6.35 


8.96 


6.39 1 


12 


9.83 


6.88 


9.80 


6.93 


9.77 


6.97 


9.74 


7.01 


12 


13 


10.65 


7.46 


10.62 


7.50 


10.. 58 


7.55 


10.55 


7.60 


13 


M 


11.47 


8.03 


11.43 


8.08 


11.40 


8.13 


11.36 


8.18 


14 


15 


12.29 


8.60 


12.25 


8.66 


12.21 


8.71 


12.17 


8.76 


15 


16 


13.11 


9.18 


13.07 


9.23 


13.03 


9.29 


12.99 


9.35 


16 


17 


13.93 


9.75 


13.83 


9.81 


13.84 


9.87 


13.80 


9.93 


17 


18 


14.74 


10.32 


14.70 


10.39 


14.65 


10.45 


14.61 


10.. 52 


18 


19 


15.56 


10.90 


15.52 


10.97 


15.47 


11.03 


15.42 


11.10 


19 


20 
21 


16.33 


11.47 


16.33 


11.54 


16.28 


11.61 


IS. 23 


11.63 


20 


17.20 


12.05 


17.15 


12.12 


17.10 


12.19 


17.04 


12.27 


21 


22 


18.02 


12.62 


17.97 


12.70 


17.91 


12.78 


17.85 


12.85 


22 


23 


18.84 


13.19 


18.78 


13.27 


18.72 


13.36 


18.67 


13.44 


23 


21 


19.66 


13.77 


19.60 


13.85 1 


19.54 


13.94 


19.48 


14.02 


24 


25 


20.48 


14.34 


20.42 


14.43 


20.35 


14.52 


120.29 


14.61 


25 


26 


21.30 


14.91 


21.23 


15.01 


21.17 


15.10 


21.10 


15.19 


26 


27 


22.12 


15.49 


22.05 


15.58 


21.98 


15.68 


21.91 


15.77 


27 


28 


22.94 


16.06 


22.87 


16.15 


22.80 


16.26 


22.72 


16.36 


28 


29 


23.76 


16.63 


23.68 


16.74 


23.61 


16.84 


23.54 


16.94 


29 


30 


24.57 


17.21 
17.78 


24.50 


17.51 


24.42 


17.42 


124.35 
25.16 


17.53 


30 
■31 


"31 


25.39 


25.32 


17.89 


25.24 


18.00 


13.11 


32 


26.21 


18.. 35 


26.13 


18.47 


26.05 


18.58 


25.97 


18.70 


32 


33 


27.03 


18.93 


26.95 


19.05 


26.87 


19.16 


26.73 


19.23 


33 


34 


27.85 


19.50 


27.77 


19.62 


27.68 


19.74 


27.59 


19.86 


34 


35 


28.67 


20.08 


28.58 


20.20 


28.49 


20.32 


128.41 


20.45 


35 


36 


29.49 


20.65 


29.40 


20.78 


29.31 


20.91 


! 29.22 


21.03 


36 


37 


30.31 


21.22 


30.22 


21.35 


30.12 


21.49 


130.03 


21.62 


37 


38 


31.13 


21.80 


31.03 


21.93 


30.94 


22.07 


30.84 


22.20 


33 


39 


31.95 


22.37 


31.85 


22.51 


31.75 


22.65 


31.65 


22.79 


39 


40 


32.77 


22.94 


32.67 


23.09 
23.66 


32.56 


23.23 
23.81 


32.46 
33.27 


23.37 
23:95 


40 

41 


41 


33.59 


23.52 


33.48 


33. 3S 


42 i 34.40 


24.09 


34.30 


24.24 


34.19 


24.39 


[34.09 


24.54 


42 


43 35.22 


24.66 


35.12 


24.82 


35.01 


21.97 


34.90 


25.12 


43 


44 36.04 


25.24 


35.93 


25.39 


35.82 


25.55 


35.71 ; 25.71 


44 


45 36.86 


25.81 


36.75 


25.97 


36.64 


26.13 


36.52 


26.29 


45 


46 137.68 


26.38 


37.57 


26.55 


37.45 


26.71 


137.33 


26.88 


46 


47 1 33.50 


26.96 


38.38 


27.13 


38.26 


27.29 


38.14 


27.46 ; 47 


48 


39.32 


27.53 


39.20 j 27.70 1 


39.08 


27.87 


38.96 


28.04 i 43 


49 


40.14 


28 . 1 1 


40.02; 28.28 


39.89 ; 23.45 


39.77 


23.63, 49 


50 


40.96 


28.68 


40.83 1 28. 86 


40.71 [29.04 


; 40.58 


29.21 


_50 



c 

3 


6 
o 

a 
a 

.2 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat. 


55] 


Deg. 


54J 


Deg. 


54.1 Deg. 


544 Oeg. 



TJIAVEESE TABLE. 



143 



5 
1 

a 

CD 

5l 


35 Deg. 


35i Deg. 


1 

35i Deg. 


-351 Deg. 


a" 

"51 


Lat. 

41.78 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

29.80 


29.25 


41.65 129.43 


41.52 


29.62 


41.39 


62 


42.60 


29.83 


42.47 30.01 


42.33 


30.20 


42.20 


30.38 


62 


63 


43.42 


3'?. 40 


43.28 


30.59 


43.15 


30.78 


43.01 


30.97 


53 


54 


44.23 


30.97 


44.10 


31.17 


43.96 


31.36 


43.82 


3 J. 55 


54 


55 


45.05 


31.55 


44.92 


31.74 


44.78 


31.94 


44.64 


32.13 


55 


56 


45.87 


32.12 


45.73 


32,32 


45.59 


32.52 


45.45 


32.72 


56 


57 


46.69 


32.69 


46.55 


32.90 


46.40 


33.10 


46.26 


33.30 


57 


58 


47.51 


33.27 


47.37 


33.47 


47.22 


33.68 


47.07 


33.89 


58 


59 


43.33 


33.84 


48.18 


34.05 


48.03 


34.26 


47.88 


34.47 


59 


60 
61 


49.15 


34.41 


49.00 


34.63 


48.85 


34.84 


48.69 


35.05 
35.64 


60 
61 


49.97 


34.99 


49.82 


35.21 


49.66 


35.42 


49.51 


62 


50.79 


35.56 


50.63 


35.78 


50.48 


36.00 


50.32 


36.22 


62 


63 


51.61 


36.14 


51.45 


36.36 


51.29 


36.58 


51.13 


36.81 


63 


64 


52.43 


36.71 


52.27 


36.94 


52.10 


37.16 


51.94 


37.39 


64 


65 


53.24 


37.28 


53.08 


37.51 


52.92 


37.75 


52.75 


37.98 


05 


66 


54.06 


37.86 


53.90 


38.09 


53.73 


38.33 


53.56 


38.56 


66 


67 


54.88 


38.43 


54.71 


38.67 


54.55 


38.91 


54.38 


39.14 1 67 I 


68 


55.70 


39.00 


55.53 


39.55 


55.36 


39.49 


55.19 


39.73 


68 


69 


56.52 


39.58 


56.35 


39.82 


56.17 


40.07 


56.00 


40.31 


69 


70 
71 


57.34 


40.15 


57.16 


40 40 


56.99 


40.65 


.56.81 


40.90 


70 

71 


58.16 


40.72 


57.98 


40.98 


157.80 


41.23 


57.62] 41.48 


72 


58.98 


41.30 


58.80 


41.55 


58.62 


41.81 


53.43 42.07 


72 


73 


59.80 


41.87 


59.61 


42.13 


59.43 


42.39 


59.24 


42.65 


73 


74 


60.62 


42.44 


60.43 


42.71 


60.24 


42.97 


60.06 


43.23 


74 


75 


61.44 


43.02 


61.25 


43.29 


61.06 


43.55 


60.87 


43.82 


75 


76 


62.26 


43.59 


62.06 


43.86 


61.87 


44.13 


61.68 


44.40 ' 76 1 


77 


63.07 


44.17 


62.88 


44.44 


i62.69 


44.71 


62.49 


44.99 


77 


78 


63.89 


44.74 


63.70 


45.02 


63.50 


45.29 


63.30 


45.57 


78 


79 


64.71 


45.31 


64.51 


45.59 


64.32 


45.88 


64.11 


46.16 


79 


80 
"81 


65.53 


45.89 


65.33 


46.17 


65.13 


46.46 


64.93 


46.74 


80 


66.35 


46.46 


66.15 


46.75 


65.94 


47.04 


65.74 


47.32 


81 


82 


67.17 


47.03 


66.96 


47.33 


66.76 


47.62 


66.55 


47.91 


82 


83 


67.99 


47.61 


67.78 


47.90 


67.57 


48.20 


67.36 


48.49 


83 


84 


68.81 


48.18 


68.60 


48.48 


68.39 


48.78 


68.17 


49.08 


84 


85 


69.63 


48.75 


69.41 


49.06 


69.20 


49.36 


68.98 


49.66 


85 


86 


70.45 


49.33 


70.23 


49.63 


70.01 


49.94 


69.80 


50.25 


86 


87 


71.27 


49.90 


71.05 


50.21 


70.83 


50.. 52 


70.61 


50.83 


87 


88 


72.09 


50 47 


71.86 


50.79 


71.64 


51.10 


71.42 


51.41 


83 


89 


72.90 


51.05 


72.68 


51.37 


72.46 


51.68 


72.23 


52.00 


89 


90 
91 


73.72 


51.62 


73.50 
74.31 


51.94 

52.52 


73.27 


52.26 


73.04 


,52.58 


90 
91 


74.54 


^2.20 


74.08 


52.84 


73.85 53.17 


92 


75.36 


52.77 


75.13 


53.10 


74.90 


53.42 


74.66 


53.75 


92 


93 


76.18 


53.34 


75.95 


53.67 


75.71 


54.01 


75.48 


54.34 


93 


94 


77.00 


53.92 


76.76 


54.25 


76.. 53 


54.. 59 


76.29 


54.92 


94 


95 


77.82 


.54.49 


77.58 


54.83 


77.34 


55.17 


77 10 


55.50 


95 


96 


78.64 


55.06 


78.40 


55.41 


78.16 


55.75 


77.91 


56.09 


96 


97 


79.46 


55.64 


79.21 


55.98 


7S 97 


56.33 


78.72 


.56.67 


97 


98 


80.28 


56.21 


80.03 


56.. 56 


79.78 


56.91 


79.53 


57.28 


98 


99 


81.10 


56.78 


80.85 


57.14 


80.60 


57.49 


80.35 


f7.84 


99 


J GO 

1 

m 
Pi 


81.92 


57.36 


81.66 


57.71 


81.41 


58.07 


81.16 


£8.42 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


s 

c 

d 


55 Deg. 


541 Deg. 


1 
54i Deg. 


54i Deg. 



144 



TRAVERST! TABLE. 





S6 Deg. 


36i Deg. 


36^ 


Deg. 


361 Deg. 


1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


"^ 


0.81 


0.69 


0.81 


0.59 


i 0.80 


0.59 


0.80 


0.60 


"l 


2 


1.62 


1.18 


1.61 


1.18 


1.61 


1.19 


1.60 


1 20 


5i 


3 


2.43 


1.76 


2.42 


1.77 


2.41 


1.78 


2.40 


1.79 


3 


4 


3.24 


2.35 


3.23 


2.37 


3.22 


2.38 


3.20 


2.39 


4 


5 


4.05 


2.94 


4.03 


2.96 


4.02 


2.97 


4.01 


2.99 


5 


6 


4.85 


3.53 


4.84 


3.55 


4.82 


3.57 


4.81 


3.59 


6 


7 


5.66 1 4.11 


5.65 


4.14 


5.63 


4.16 


5.61 


4.19 


7 


8 


6.47! 4.70 


6.45 


4.73 


6.43 


4.76 


6.41 


4.79 


8 


9 


7.28 1 5.29 


7.26 


5.32 


7.23 


5.35 


7.21 


5.3S 


9 


10 
11 


8.09 1 5.88 


8.06 


5.91 


8.04 


5.95 


8.01 


5.98 


10 
"ll 


8.90, 6.47 


8.87 


6.50 


8.84 


6.54 


8.81 


6.58 


12 


9.71 


! 7.05 


9.68 


7.10 


9.65 


7.14 


9.61 


7.18 


12 


13 


10.52 


7.64 


10.48 


7.69 


10.45 


7.73 


10.42 


7.78 


13 


14 


11.33 


8.23 


11.29 


8.28 


11.25 


8.33 


11.22 


8.38 


14 


15 


12.14 


8.82 


12.10 


8.87 


12.06 


8.92 


12.02 


8.97 


15 


16 


12.94 


9.40 


12.90 


9.46 


12.86 


9.52 


12.82 


9.57 


16 


17 


13.75 


9.99 


13.71 


10.05 


13.67 


10.11 


13.62 


10.17 


17 


18 


14.56 


10.58 


14.52 


10.64 


14.47 


10.71 


14.42 


10.77 


18 


19 


15.37 


11.17 


15.32 


11.23 


15.27 


11.30 


15.22 


11.37 


19 


20 
21 


16.1.8 


11.76 


16.13 


11.83 


16.08 


11.90 


16.03 


11.97 


20 
21 


16.99 


12.34 


16.94 


12.42 


16.88 


12.49 


16.83 


12.56 


22 


17.80 


12.93 


17.74 


13.01 


17.68 


13.09 


17.63 


13.16 


22 


23 


18.61 


13.52 


18.55 


13.60 


18.49 


13.68 


18.43 


13.76 


23 


24 


19.42 


14.11 


19.35 


14.19 


19.29 


14.28 


19.23 


14.36 


24 


25 


20.23 


14.69 


20.16 


14.78 


20.10 


14.87 


20.03 


14.96 


25 


26 


21.03 


15.28 


20.97 


15.37 


20.90 


15.47 


20.83 


15.56 


26 


27 


21.84 


15.87 


21.77 


15.97 


21.70 


16.06 


21.63 


16.15 


27 


28 


22.65 


16.46 


22.58 


16.56 


22.51 


16.65 


22.44 


16.75 


28 


29 


23.46 


17.05 


23.39 


17.15 


23.31 


17.25 


23.24 


17.35 


29 


30 
31 


24.27 


17.63 


24.19 


17.74 


24.12 


17.84 


24.04 


17.95 


30 
31 


25.08 


18.22 


25.00 


18.83 


24.92 


18.44 


24.84 


18.55 


32 


25.89 


18.81 


25.81 


18.92 


25.72 


19.03 


25.64 


19.15 


32 


33 


26.70 


19.40 


26.61 


19.51 


26.53 


19.63 


26.44 


19.74 


33 


34 


27.51 


19.98 


27.42 


20.10 


27.33 


20.22 


27.24 


20.34 


34 


35 


28.32 


20.57 


28.23 


20.70 


28.13 


20.82 


28.04 


20.94 


35 


36 


29.12 


21.16 


29.03 


21.29 


28.94 


21.41 


28.85 


21.54 


36 


37 


29.93 


21.75 


29.84 


21.88 


29.74 


22.01 


29.65 


22.14 


37 


38 


30.74 


22.34 


30.64 


22.47 


30.55 


22.60 


30.45 


22.74 


38 


89 


31.55 


22.92 


31.45 


23.06 


31.35 


23.20 


31.25 


23.33 


39 


40 
~41 


32.36 


23.51 


32.26 


23.65 


32.15 


23.79 


32.05 


23.93 


40 
41 


33.17 


24.10 


33.06 


24.24 


32.96 


24.39 


32.85 


24.53 


42 


33.98 


24.69 


33.87 


24.83 


33.76 


24.98 


33.65 


25.13 


42 


43 


34.79 


25.27 


34.68 


25.43 


34.57 


25.68 


34.45 


25.73 


43 


44 


35.60 


25.86 


35.48 


26.02 


35.37 


26.17 


35.26 


26.33 


44 


45 


30.41 


26.45 


36.29 


26.61 


36.17 


26.77 


36.06 


26.92 


45 


46 


37.21 


27.04 


37.10 


27.20 


36.98 


27.36 


36.86 


27.52 


46 


47 


38.02 


27.63 


37.90 


27.79 


37.78 


27.96 


37.66 


28.12 


47 


48 


38.83 


28.21 


38.71 


28.38 


38.59 


28.55 


38.46 


28.72 


48 


49 


39.64 


28.80 


39*. 52 


28.97 


39.39 


29.15 


39.26 


29.32 


49 


d 1 


40.45 


29.39 


40.32 


29.57 


40.19 


29.74 


40.06 


29.92 


50 

d 
u 

a 


Dcp. 


Lat. 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat. 


541 


)eg. 


53} I 


>e. 


53i Deg. 


53i Deg. 



TRAVERSE TABLE. 



145 



s 

? 

61 


36 Deg. 


36i Deg. 


36i Deg. 


361 Deg. 


"51 


Lat. Dep. 


Lat. 


Dep. 


Lat 


Dep 


Lat. 


Dep. 


141.26 '29.98 


41.13 


30.16 


41.00 30.34 


40 86 


30.51 


52 


42 07:30.56 


41.94 


30.76 


41.80 30.93 


41 67 


31.11 


52 


53 


42.88 131.15 


142.741 31.34 


42.60 31.53 


42.47 


31.71 


53 


54 


43.69 131.74 


43.56 


31.93 


43.41 132.12 


43.27 


32.31 


54 


55 


44.50 ! 32.33 


44.35 


32.52 


44.21 32.72 


44.07 


32.91 


55 


56 


45.30 1 32.92 


45.16 


33.11 


46.02 33.31 


44.87 


33.51 


5G 


57 


46.11 33.50 


45.97 


33,70 


46.82 33.90 


45.67 


34.10 


57 


58 


46.92 34.09 


46.77 


34.30 


46.62 34.60 


46.47 


34.70 


58 


59 


47.73 34.68 


47.58 


34.89 


147.43 35 09 


47.27 


35.30 


59 


60 
'61 


48.54! 35.27 


48.39 


35.48 


148.23 


i 35.69 


48.08 


35.90 


60 
61 


49.35 


35.85 


49.19 


36.07 


! 49.04 


36.28 : 48.88 


36.50 


62 


50.16 


36.44 


50.00 


36.66 


149.84 


36.88 [49.68 


37.10 


62 


63 


50.97 


37.03 


50.81 


37.25 


150.64 


37.47 


50.48 


37.69 


63 


S4 


51.78 


37.62 


61.61 


37.84 


,161.45 


38.07 


51.28 


38.29 


64 


65 


52.59 


38,21 


52.42 


38.44 


62.25 


3S.66 


62.08 


38.89 


65 


66 


53.40 


38.79 


53.23 


39.03 


153.05 


39.26 


52.88 


39.49 


66 


67 


54.20 


39.38 


64.03 


39.62 


153.86 


39.85 


53.68 


40.09 


67 


68 


55.01 


39.97 


54.84 


40.21 


154.66 


40.45 


54.49 


40.69 


68 


69 


55.82 


40.56 


55.64 


40.80 


156.47 


41.04 


55.29 


41.23 


69 


70 
71 


56.63 


41.14 


50.45 


41.39 


156.27 


41.64 


66.09 


41.88 


70 

71 


57.44 


41.73 


57.20 


41.98 


i 67.07 ; 42.23 166.89 


42.48 


72 


58.25 


42.32 


58.06 


42.57 


i 57.88 142.83 J 57.69 


43.08 


72 


73 


69.06 


42.91 


58.87 


43.17 


j 68.68 


43.42 il 58.49 


43.68 


73 


74 


59.87 


43.50 1 


59.68 


43.76 


59.49 


44.02 


'69.29 


44.28 


74 


75 


60.68 


44.08 


60.48 


44.36 


60.29 


44.61 


60.09 


44.87 


75 


76 


61.49 


44.67 1 


61.29 


44.94 


61.09 


45.21 


60.90 


45.47 


70 


77 


62.29 


45.26 


62.10 


45.63 


61.90 


45.80 


61.70 


46.07 


77 


78 


63.10 


45.85 


62.90 


46.12 


62.70 


46.40 


62.50 


46.67 


78 


79 


63.91 


46.43 


63.71 


46.71 


63.50 


46.99 


63.30 


47.27 


79 


80 
81 


64.72 


47.02 


64.52 


47.30 


64.31 


47.59 


64.10 


47.87 


80 
81 


65.53 


47.61 


65.32 


47.90 


65.11 


48.18 


64.90 


48.46 


82 


66.34 


48.20 


66.13 


48.49 


65.92 


48.78 


65.70 


49.06 


82 


83 


67.15 


48.79 1 


66.93 


49.08 


66.72 


49.37 


66.50 


49.66 


83 


84 


67.96 


49.371 


67.74 


49.67 


67.52 


49.97 


67.31 


50.26 


84 


85 


68.77 


49.96 1 


68.55 


60.26 


68.33 


50.56 


68.11 


60.86 


85 


86 


69.58 


50.55; 


60.35 


50.85 


69.13 


51.15 


68.91 


61.46 


86 


87 


70.38 


51.141 


70.16 


61.44 


69.94 


51.75 


69.71 


52.06 


87 


88 


71.19 


51.73 1 


70.97 


52.04 


70.74 


52.34 


70.51 


52.65 


88 


89 


72.00 


52.31 j 


71.77 


62.63 


71.54 


52.94 


71.31 


53.25 


89 


90 

91 


72.81 


52.90] 


72.58 
73.39 


63.22 


72.35 


53.53 


72.11 


53.85 


90 
91 


73.62 53.49 j 


63.81 


73.16 


54.13 


72.91 


54.45 


92 


74.43 64.08 


74.19 


64.40 


73.96 


54.72 


73.72 


65.05 


92 


93 1 75.24 154.66 1 


75.00 


54.99 


74.76 


55.32 


74.62 


65.64 


93 


94 76.05 '55.25! 


75.81 


65.58 


75.56 


55.91 


76.32 


50.24 


94 


95, 


76.86 


55.84 


76.61 


66.17 


76.37 


56.51 


76.12 


56.84 


95 


96' 


77.67 


56.43 


77.42 


56.77 


77.17 


57.10 


76.92 


57.44 


96 


97! 


78.47 


57.02 


78.23 


57.36 


77.97 


57.70 


77.72 


58.04 


97 


98 1 


79.28 


67.60 


79.03 


57.95 


78.78 


58.29 


78.52 


68.64 


98 


99; 


80.09 58.19 


79.84 


58.54 


79.58 


58.89 


79.32 


59.23 


99 


100 1 

1 

Q 


80.90 158.78 


80.64 


59.13 


80.39 


59.48 


80.13 


59.83 


100 

5 


Dep. 


Lat. 1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep 


Lat. 


54 Deg. 


531 Degr. 


53i Deg. 


53i Dog. 



146 



TRAVERSE TABLE. 



1 


37 Deg. 1 


37^ Deg. 


37i Deg. 


371 Deg. 


C 
n" 

J 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep 

"oTeT 


0.80 


0.60 


0.80 


0.61 


0.79 


0.61 


0.79 


2; 1.60 


1.20 


1.59 


1.21 


1.59 


1.22 


1.58 


1.22 


2 


3; 2.40 


1.81 


2.39 


1.82 


2.38 


1.83 ; 


2.37 


1.84 


3 


4 1 3.19 


2.41 


3.18 


2.42 


3.17 


2 43 i 


3.16 


2.45 


4 


51 3.99 


3.01 


3.98 


3.03 


3.97 


3.04: 


3.95 


3.06 


R 


6 


4.79 


3.61 


4.78 


3 63 


4.76 


3.65! 


4.74 


3.67 


6 


7 


5.59 


4.21 


5.57 


4.24 


5.. 55 


4.26 


6.53 


4.29 


7 


8 


6.39 


4.81 


6.37 


4.84 


6.35 


4.87 1 


6.33 


4.90 


8 


9 


7.19 


5.42 


7.16 


5 45 


7.14 


5.48 1 


7.12 


5.51 


9 


10 

11 


7.99 


6.02 


7.98 


6.05 


7.93 

8.73 


6.09 
6.70 


7.91 


6.12 


10 
11 


8.78 


6.62 


8.76 


6.66 


8.70 


6.73 


12 


9.58 


7.22 


9.55 


7.26 


9.52 


7.31 


9.49 


7.35 


12 


13 


10.38 


7.82 


10.35 


7.87 


10.31 


7.91 


10.28 


7.96 


13 


14 


11.18 


8.43 


11.14 


8.47 


11.11 


8.52 


11.07 


8.57 


14 


15 


11.98 


9.03 


11.94 


9.03 


11.90 


9.13 


11.86 


9.18 


15 


16 


12.78 


9.63 


12.74 


9.68 


12.69 


9.74 


12.65 


9. 80 


16 


17 


13.58 


10.23 


13.53 


10.29 


13.49 


10.35 


13.44 


10.41 


17 


18 


14.38 


10.83 


14.33 


10.90 


14.23 


10.96 


14.23 


11.02 


18 


19 


15.17 


11.43 


15.12 


11.50 


15.07 


11.57 


15.02 


11.63 


19 


20 
21 


15.97 


12.04 


15.92 


12.11 


15.87 


12.18 


15.81 


12.24 


20 
21 


16.77 1 12.64 


16.72 


12.71 


16.66 


12.78 


16.60 


12.80 


22 


17.57 


13.24 


17.51 


13.32 


17.45 


13.39 


17.40 


13.47 


22 


23 


18.37 


13.84, 


18.31 


13.92 


118.25 


14.00 


18.19 


14.08 


23 


24 


19.17 


14.44 


19.10 


14.53 


119.04 


14.61 


18.98 


14.69 


24 


25 


19.97 


15.05 


19.90 


15.13 


19.83 


15.22 


19.77 


15.31 


25 


26 


20.76 


15.65 


20.70 


15.74 


20.63 


15.83 


20.56 


15.92 


26 


27 


21.56 


16.25 


21.49 


16.34 


21.42 


16.44 


21.35 


16.53 


27 


28 


22.38 


16.85 


22.29 


16.95 


22.21 


17.05 


22.14 


17.14 


28 


29 


23.16 


17.45 


23.08 


17.55 


23.01 


17.65 


22.93 


17.75 


29 


30 
31 


23.96 


18.05 


23.88 


18.16 


23.80 


18.26 


23.72 


18.37 


30 
31 


24.76 


18.06 


24.68 


18.76 


24.59 


18.87 


24.51 


18.98 


32 


25.56 


19.26 


25.47 


19.37 


25.39 


19.43 


25.30 


19.59 


33 


33 


20.35 


19.86 


26.27 


19.97 


26.18 


20.09 


26.09 


20.20 


33 


34 


27.15 


20.46 


27.06 


20.58 


26.97 


20.70 


26.88 i 20.82 


34 


35 


27.95 


21.06 


27.86 


21.19 


27.77 


21.31 


27.67 121.43 


35 


36 


28.75 


21.67 


28.66 


21.79 


28.56 


21.92 


28.46 1 22.04 


36 


37 


29.55 


22.27 


29.45 


22.40 


29.. 35 


22.52 


29.26 i 22.65 


37 


38 


30.35 


22.87 


30.25 


23.00 


30.15 


23.13 


30.05 1 23.26 


33 


39 


31.15 


23.47 


31.04 


23.61 


30.94 


23.74 


30.84! 23.88 


39 


40 
"41 


31.95 


24.07 


31.84 


24.21 


31.73 


24.35 


31.03 24.49 
32.42 25.10 


40 
41 


32.74 


24.67 


32.64 


24.82 


32 53 1 24.96 


42 


33.54 


25.28 


33.43 


25.42 


33 32 


35.57 


33.21 1 25.71 ' 42 


43 


34.34 25.88 


34.23 


26.03 


34.11 


26.18 


34.00; 26.33, 43 


44 


35.14 20.48 


35.02 


26.63 


34.91 


26.79 


34.79 26.94 


44 


45 


35.94 27,08 


35.82 


27.24 


35.70 


27.39 


35.53 27.. 55 


45 


40 36.74 127.68!! 36.62 


27.84 


36.49 1 28.00 


36.37 28.16 


46 


47 37.54 


28.29 


1 37.41 


28.45 


37.29 ; 28.61 


37.16 28 77 


47 


48 


3S.33 


23.89 


I 38.21 


29.05 


38.08 ! 29.22 


37.95 29.39 


. 48 


49 


39.13 


29.49 


.39.00 


29.66 


38.87 29.83 


38.74 30.00 


i 49 


50^ 

8 
1 

U4 


39.93 


30.09 


39.80 


30.26 


39.67 ,30.44 


39.53' 30.61 


50 

1 

.a 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. 


53 


Deg. 


521 


Deg. 


52i Deg 


52i Deg. 

1 



TRAVERSE TABLE. 



147 



3 
? 

61 


3? Deg. 


374 Deg. 


37i Deg. 


371 Deg. 


5 

1 

61 


Lat. 


Dop. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

40.33 


Dep. 

31.22 


40.73 


30.69 


40.60 


30.87 


40.46 


31.05 


52 


41.53 


31.29 


41.39 


31.48 


41.25 


31.66 


41.12 


31.84 


62 


63 


42.33 


31.90 


42.19 


32.08 


42.05 


32.26 


41.91 


32.45 


53 


64 


43.13 


32.50 


42.98 


32.69 


42.84 


32.87 


42.70 


33.06 


54 


65 


43.92 


33.10 


43.78 


33.29 


43.63 


33.48 


43.49 


33.67 


55 


66 


44.72 


33.70 


44.58 


33.90 


44.43 


34.09 


44.28 


34.28 


66 


67 


45.52 


34.30 


45.37 


34.50 


45.22 


34.70 


45.07 


34.90 


67 


68 


46.32 


34.91 


40.17 


35.11 


46.01 


35.31 


46.86 


85.51 


58 


59 


47.12 


35.51 


46.96 


35.71 


46.81 


35.92 


46.65 


36.12 


69 


60 
"~61 


47.92 


36.11 


47.76 


36.32 


47.60 


36.53 


47.44 


36.73 


60 
'61 


48.72 


36.71 


48.66 


36.92 


48.39 


37.13 


48.23 


37.35 


62 


49.52 


37.31 


49.35 


37.53 


49.19 


37.74 


49.02 


37.96 


62 


63 


50.31 


37.91 


50.15 


38.13 


49.98 


38.35 


49.81 


38.57 


63 


64 


51.11 


38.52 


60.94 


38.74 


50.77 


38.96 


.50.60 


39.18 


64 


65 


51.91 


39.12 


51.74 


39.34 


51.67 


39.57 


51.39 


39.79 


66 


66 


52.71 


39.72 


52.64 


39.95 


62.36 


40.18 


52.19 


40.41 


66 


67 


53.51 


40.32 


53.33 


40.65 


53.15 


40.79 


62.98 


41.02 


67 


68 


54.31 


40.92 


54.13 


41.16 


53.95 


41.40 


53.77 


41.63 


08 


69 


65.11 


41.53 


54.92 


41.77 


54.74 


42.00 


54.56 


42.24 


09 


70 
'71 


65.90 


42.13 


65.72 


42.37 


65.53 
66.33 


42.61 


65.35 


42.86 


70 
'71 


56.70 


42.73 


66.62 


42.98 


43.22 


56.14 


43.47 


72 


67.50 


43.33 


57.31 


43.58 


57.12 


43.83 


66.93 


44.08 


72 


73 


58.30 


43.93 


.58.11 


44.19 


57.91 


44.44 


57.72 


44.69 


73 


74 


59.10 


44.53 


68.90 


44.79 


.58.71 


45.05 


68.51 


45.30 


74 


75 


59.90 


45.14 


59.70 


45.40 


.59.60 


45.66 


69.30 


45.92 


75 


76 


60.70 


45.74 


60.60 


46.00 


60.29 


46.27 


60.09 


46.53 


76 


77 


61.49 


46.34 


61.29 


46.61 


61.09 


46.87 


60.88 


47.14 


77 


78 


62.29 


46.94 


62.09 


47.21 


61.88 


47.48 


61.67 


47.75 


78 


79 


63.09 


47.64 


62.88 


47.82 


62.67 


48.09 


62.46 


48.37 


79 


80 
81 


63.89 
64.69 


48.15 


63.68 


48.42 


63.47 


48.70 


63.26 


43.98 


80 
81 


48.75 


64.48 


49.03 


64. 2T) 


49.31 


64.05 


49.59 


82 


65.49 


49.35 


65.27 


49.63 


65.05 


49.92 


64.84 


50.20 


82 


83 


66.29 


49.95 


66.07 


60.24 


65.85 


50.53 


65.63 


50.81 


83 


84 


67.09 


50.55 


66.86 


.50.84 


66.64 


61.14 


66.42 


61.43 


84 


85 


67.88 


51.15 


67.66 


51.45 


67.43 


51.74 


67.21 


52.04 1 86 


86 


68.68 


51.76 


68.46 


52.06 


68.23 


62.35 


68.00 


62.65 i 86 


87 


69.48 


52.36 


69.25 


52.66 


69.02 


52.96 


68.79 


63.26. 87 


88 


70.28 


52.96 


70.05 


53.27 


69.82 


63.57 


69.58 


53.88 


88 


89 


71.08 


53.56 


70.84 


53.87 


70.61 


54.18 


70.37 


54.49 


89 


90 
91 


71.88 


54.16 


71.64 


64.48 


71.40 


64.79 


71.16 


65.10 


90 


72.68 


54.77 


72.44 


65.08 


72.20 


55.40 


71.96 


65.71 


91 


92 


73.47 


55.37 


73.23 


55.69 


72.99 


56.01 


72.74 


.56.32 


92 


93 


74.27 


55.97 


74.03 


66.29 


73.78 


56.61 


73.53 


56.94 


93 


94 


75.07 


66.57 


74.82 


66.90 


74.58 


67.22 


74.32 


67.65 


94 


95 


75.87 


57.17 


75.62 


57.60 


75.37 


67.83 


75.12 


58.16 


95 


90 


76.67 


57.77 


76.42 


68.11 


76.16 


58.44 


75 91 


68.77 


96 


97 


r7.47 


68.38 


77.21 


68.71 


76.96 


69.05 


76 70 


69.39 


97 


98 


78.27 


58.98 


78.01 


69.32 


77.75 


59.66 


77.49 


60.00 


98 


99 


79.06 


.69.58 


78.80 


69.92 


78.64 


60.27 


78.28 


60.61 


99 


100 

d 

1 


79.86 


60.18 


79.60 


60.53 


79.34 


60.88 


79.07 


61.22 


100 

i 

Q 


Dcp. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


53 Deg. 


521 Deg. 


52^ Deg. 


52i Deg. 



24 



148 



TRAVERSE TABLE. 






3ft Dag. \ 

1 


38i Deg. 


38i Deg. 

1 


381 Dtg. 


X 

"1 




Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


i* 0.79 


"0.62" 


0.79 1 0.62 


0.78 


0.62 


0.78 


0.63 1 


2 1.58 


1.23 


1.57 1 1.24 


1.57 


1.24 


1.56 


1.25 


2 


3 1 2.36 


1.85 


2.36 1.86 


2.35 


1.87 


2.34 


1.88 


3 


4; 3.15 


2.46 


3.14 2.48 


3.13 


2.49 


3.12 


2.50 


4 


5 3.94 


3.08 


3.93 3.10 


3.91 


3 11 


3.90 


3.13 


5 


6 


4.73 


3.69 i 


4.71 3.71 


4.70 


3.74 


4.63 


3.76 


3 


7 


5.. 52 


4.31 1 


5.50; 4.33 


5.48 


4.36 


5.46 


4.38 


7 


8 


6.30 


4.93! 


6.28 


4.95 


6.26 


4.98! 


6.24 


5.01 


3 


9 


7.09 


6 54! 


7.07 


5.57 


7.04 


5.60': 7.02 


5.63 


n 


10 


7.88 


6.161 


7.85 
8.64 


6.19 
6.81 


7.83 6.23 !i 7.80 


6.20 


"11 


8.67 


6.77 


8.61 1 6.85 II 8. .58 


6.89 


12, 9.46 


7.39 


9.42 


7.43 


9.39 1 7.47I! 9.36 


7.51 12 


13 1 10.24 


8.00 


10.21 


8.05 


10.17i 8.09!! 10.14 


8.14 13 


14 11.03 


8.62 


10.99 


8.67 


10.96 i 8.72;; 10.92 


8.70 14 


75 11.82 


9.23 


11.78 


9.29 


11.74] 9.34!' 11.70 


9.39 15 


16 j 12.61 


9.85 


12.57 


9.91 


12.52 9.96,12.48 


10.01 1 16 


17 1 13.40 


10.47: 


13.35 


10.52 


13.30! 10.58^ 13.26 


10.64 17 


18 ! 14.18 


11.08 


14.14 


11.14 


14.091 11.21 1 14.04 


11.27 i 18 


19 : 14.97 


11.70 


14.92 1 11.76 


14.87 i 11.83 1 14.82 


11.89 1 19 


20 115.76 

21 1 16.55 


12.31 ; 
12.93 


15.71 1 12.38 


15.65! 12.45:' 15.60 


12.52 i 20 


16.49 


13.00 


16.43 1 13.07 


16.38] 13.14 i 21 


22 ' 17.34 


13.54 


17.28 


13.62 


17.22 1 13.70 


17.161 13.77 22 


23 i 18.12 


14.16 


18.06 


14.24 


18.00 1 14.32 


17.941 14.40 23 


24 118.91 


14.78 


18.85 


14.86 1 


18.78 


14.94 


18.72 115.02 24 


25 19.70 


15.39 


19.63 


15.48 


19.57 


15.56 


19.50] 15.65 25 


26 


20.49 


16.01 


20.42 


16.10 


20.35 


16.19 


20.28 16.27 26 


27 


21.23 


16.62 


21.20 


16.72 


21.13 


16.8] 


21.06 16.90 27 


28 


22.06 


17.24 


21.99 17.331 


21.91 


17.43 


21.84 1 17.53 ' 23 


29 


22.85 


17.85 


22.77 17.95 


22.70 


18.05 


22.62 1 18.15 ; 29 


30 23.64 


18.47 


23.56 18.57 


23.48 1 18.63 
24.26 1 19.30 


23.40; 13.78 ! 30 
24.13 ] 19.40 i 31 


31 24.43 


19.09 


124.34 1 1^.19 


32 25.22 


19.70 


25.13 ! 19.81 


25.041 19.92 


24.96 [20.03 ' 32 


33 26.00 


20.32 


, 25.92' 20.43!! 25.83 1 20.54 


25.74 1 20.66 1 33 


34 ! 26.79 


20.93 


26.70 21.05 


26.61 ! 21.17 


26.52 121.23 | 34 


35 27.58 


21.55 


27.49 121.67 


27.39! 21.79 


27.30 21.91 ! 35 


36 


23.37 1 22.16 


28.27 122.29 


23.17 


22.41 


28.08 22.53 \ 36 


37 


29.16 


22.78 


29.06 i 22.91 


28.96 


23.03 


23.86 23.16 1 37 


38 


29.94 


23.40 


' 29.84 1 23.53 


29.74 


23.66 '29.64! 23.79 i 38 


39 


30.73 


24.01 


! 30.63 24. Uji 30.52 


24.23 30.42 124.41 ' 39 


40 


31.52 


24.63 


1 31.41 ! 24.76 


31.30 


24.90 31.20 1 25.04 40 


41 132.31 


25.24 


i 32.20 25.38 


32.09 


25.52 ■■ 31.98 


25.66 : 41 


42 33.10 


25.86 


132.98 26.00 ' 32.87 


26.15 32.76 


26.29 1 42 


43 33.88 


26.47 


133.77 26.62 33.65 


26.77 33.53 


26.911 43 


44 134.67 127.09 


34.55 27.24,1 31.43 


27.39 34.31 


27.54 44 


45 35 46 


127.70 


35.34 27.86 35.22 


28.01 ii35.09 


28.17 1 45 


46 36.25 (28.32 


36.12 28.48 1! 36.00 


28.641 35.87 


28.79 46 


47 37.04 


128.94 


36.91 ; 29.10 


36.78 


2J.26: 36.65 


,2;^. 42 47 


48 '37.82 


129.55 


37.70 1 29.72 


37.57 


29.83 1' 37.43 


J 30.04 


1 4^ 


49 i 38.61 


30.17 


38.48 30.34 


38.35 


30.50 1-38.21 


30.67 


i 49 


60 139.40^ 


[30.78 


39.27 30.95 


39.13 


31 13i;38.S9 


31. 3Q 


i! 

1 

1 


8 
1 

.52 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


52. 


Deg. 


-511 Deg. 


5U Deg. 


5U Do-. 



TRAVERSE TABIE. 



149 



Ti 


38 Deg. 


m Deg. 


38i Deg. 


3S| Deg. 


C 

I 


Lat. 


Dep. 


Lat. 
40.05 


.Dep. 
31.57 


1 Lat. j Dep. 


Lat, 


Dep. 


40.19 131.40 


39.91 31.75 


39.77 1 31.92 i 61 1 


62 


40.98 132.01 


40.84 


1 32.19 


! 40.70 132.3?' ! 40.55 132.55 ; 52 


63 


41.76 


32.63 


41.62 


32.81 


1 41.48 132.99 1:41.33 33.1?' 53 


64 


42.55 


33.25 


42.41 


'33.43 


! 42.26 33.62 li 42.11 : 33.80 54 


65 


43.34 


33.86 


43.19 134.05 


43.04 34.24 142.89 34.43 ,')5 


66 


44.13 


34.48 


43.98 I 34.67 


43.83 34.86 ; 43.67 35.05 56 


57 


44.92 


35.09 


44.76 i 35.29 


4-4.61 1 35.48 44.45 135.68 .57 


68 


45.70 


35.71 


45.55 j 35.91 


145.39 36.11 l! 45.23 36.30 58 


69 


46.49 


36.32 


46.33 136.53 


146.17 136.73'! 46.01 36.93 i 59 


60 
61 


47.28 


36.94 


47.12 137.15 


146.96 137.35 

147.74 , 37.97 


; 46.79! 37.56 


60 

61 


48.07 


37.56 


47.90 37.76 


47.57 1 38.18 


62 


48.86 


38.17 


48.69 33.38 


j 48.52 i 38.60 '48.35 1 33.81 


62 


63 


49.64 


38.79 


49.47 139.00 


49.30 139.22 '49.13! 39.43 


63 


64 


50.43 


39.40 


50.26 39.62 


150.09 39.84 149.91 


40.06 


64 


65 


51.22 


40.02 


51.05 140.24 


150.87 40.46 '50.69 


40.68 i 65 


66 


52.01 


40.63 


51.83 140.86 


51.65 41.09 51.47 


41.31 , 66 


67 


62.80 


41.25 


52.62 141.48 


52.43 41.71 152.25 


41.94 1 67 


68 


53.58 


41.86 


1 53.40 1 42.10 


: 53.22 42.33 ] 53.03 i 42.56 ! 63 | 


69 


54.37 


42.48 


! 54.19 142.72 


54.00 142.95 153.81 


43.19 69 1 


70 
71 


55.16 


43.10 


54.97 43.34 
55.76 43.96 


54.78 143.58 
55.57 144.20 


'54.59 


43.81 


70 


55.95 


43.71 


55.37 


44 44 


71 


72 


56.74 


44.33 


56.54! 44.57 


56.35 44.82 56.15 


45 07 ! 72 


73 157.52 


44.94 


57.33 45.19 


57.13 145.44 '56.93 


45.69! 73 


74 


58.31 


45.56 


[58.11 45.81 


157.91 148.07 


157.71 


46.32 j 74 


75 


59.10 


46.17 


58.90 46.43 


58.70 146.69 


158.49 


46.94 1 75 


76 


59.89 


46.79 


59.08 47.05 


59.48 


47.31 


159.27 


47.57! 76 


77 


00.68 


47.41 


60.47 ., 47.67 


'69.26 


47.93 


160 05 


48.20' 77 


78 


61.46 


48.02 


61.25 148.29 


61.04 


43.56 


!60 83 1 48.82 1 78 


79 


62.25 


48.64 


62.04! 48.91 


61.83 


49.18 


61.61 49.45! 79 


80 
81 


63.04 


49.25 


62.83 


49.53 
50.15 


62.61 


49.80 
50.42 


62.39 1 50.07! 80 


63.83 


49.87 


63.61 


63.39 


63.17 


50.70 i 81 


82 


64.02 


50.43 


64.40 50.77 


64.17 


51.05 


63.95 


51.33 1 82 


83 


65.40 


51.10 


65.18 51.38 


64.96 151.67 


1 64.73 


51.95 1 83 


84 


66.19 


51.72 
52.33 


65.97 52.00 


65.74 152.29 


65.51 


52.58 i 84 


85 


60.98 


66.75 152.62 


66.52 


52.91 


'66.29 


53.20 ! 85 


86 


67.77 


52.95 


67.54 


53. .24 


67.30 


53.54 


'67.07 


53.83! 86 


87 


68.56 


53.56 


68.32 


53.86 


68.09 


54.16 


'67.85 


54.46 1 87 


88 


69.34 


54.18! 


69.11 


54.48 


68.87 


54.78 


68.63 


65.08 1 88 


89 


70.13 


54.79 i 


69.89 


55.10 


69.65 


55.40 


69.41 


55.71 89 


90 
91 


70.92 


55.41 i 
56.03; 


70.68 


55.72 


70.43 


56.03 


70.19 


.'V6.33I 


90 


71.71 


71.46 


56.34 


71.22 


56.65 


70.97 


£6.96 i 


91 


92 


72.50 


56.64' 


72.25 


56.96 72.00 


57.27 


71.75 


57.53 ; 92 


93 


73.23 


57.26: 


73.03 


57.58 72.73 157.89 


72.53 


53.21 93 


94 


74.07 


57.87 1 


73.82 '58.19 


73.57 153.52 


73.31 


58.84 1 94 


95 


.'4.86 i 58.49 1 


74.81 '58.81 


74.35 159.14 


74.09 


59.46' 95 


96 


75.65 i 69.10 1 


75.39 i 59.43 


75.13 159.76 


74.87 


60. 09 96 


97 


76.44 159.72! 


76.18 160.05 


75.91 160.38 


75.65 


60.71 97 


93, 


77.22 i6u.33l 


76.96 


60.67 


76.70 61.01 


76.431 


61. 341 98 


99 


73.01 


60.95 


77.75 


61.29 


77.48 61.63 


77.21 1 61.97 1 99 1 


100 

M 


78.80 


61.57 


78.53 


61.91 


78.26 '62.25 1 


77.99 62.59; 


100 


Dep. 


Lat. 


Dep. 


Lat., 


Dep. Lat. 


Dep. 1 Lat. i 


c 


52 1 


>eg. 


511 Deg. ! 


51 i Deg. 




5U] 


^g 


1 

(5 



150 



TRAVERSE TABLE. 



2 

5 
P 

3 

s 
' 1 


39 Deg. 


394 Deg. 


m Deg. 


39t Deg. 


O 

£• 

3 
O 
? 

^1 


Lat. 
0.78 


Dep. 


Lat. 


Dep. 


II Lat. 


Dep. 


Lat. 


Dep. 


0.63 


0.77 


0.63 1 0.77 


0.64 


0.77 


64 


2 


1.55 1.26 


1.55 


1.27 j 1.54 


1.27 


1.54 


1.28 


2 


3 


2.33 1.89 


2.32 


1.90 ! 2.31 


1.91 


2.31 


1.92 


3 


4 


3.11 2.52 


3.10 


2.53 3.09 ( 2.54 


3.08 


2.56 


4 


6 


3.89 


3.15 


3.87 


3.16; 3.86 


3.18 


3.84 


3.20 


6 


8 


4.66 


3.78 


4.65 


3.80] 4.83 


3.82 


4.61 


3.84 


ft 


7 


5.44 


4.41 


5.42 


4.43 !l 5.40 


4.45 


5.38 


4.48 


7 


8 


6.22 


5.03 


6.20 


5.06 |! 6.17 
5.69 6.94 


5.09 


6.15 


5.12 


8 


9- 6.99 


5.68 


6.97 


5.72 


6.92 


5.75 


9 


\0 

11 


7.77 


6.29 
6.92 


7.74 


6.33 i! 7.72 


6.36 


7.69 


6.. 39 


10 

11 


8.55 


8.52 


6.96; 8.49 


7.00 


8.46 


7.03 


12 


9.33 


7.55 


9.29 


7.59 9.26 


7.63 


9.23 


7.67 


12 


13 


10.10 


8.18 


10.07 


8.23 11 10.03 


8.27 


9.99 


8.31 


13 


14 1 10.88 


8.81 


10.84 


8.86 h 10,80 

9.49 1 11.57 


8.91 


10.76 


8.95 


14 


15 11.66 


9.44 


11.62 


9.54 


11. .53 


9.59 


15 


16 12.43 


10.07 


12.39 


10.12 11 12.35 


10.18 


12.30 


10.23 


16 


17 13.21 


10.70 


13.16 


10.76 ll 13.12 


10.81 


13.07 


10.87 


17 


18 ! 13.99 


11.33 


13.94 


11.39 |; 13.89 


11.45 


13.84 


11.51 


18 


19 1 14.77 


11.96 


14.71 


12.02 I 14 06 


12.09 


14.61 


12.15 


19 


20 I 15.54 


12.59 


15.49 


12.65 }i 15.43 


12.72 


15.38 
16.15 


12.79 
13.43 


20 

21 


21 ' 16.32 


13.22 


16.28 


13.29 i' 16.20 


13. .36 


22 


17.10 13.84 


17.04 


13.92 


i 16.93 


13.99 


16.91 


14.07 


22 


23 


17.87 14.47 


17.81 


14.55 


1 17.75 


14.63 


17.63 


14.71 


23 


24 


18.65 15.10 ,18.59 


15.18 


1 18.52 


15.27 


18.45 


15,35 


24 


25 


19.43 15.73 


'19.36 


15.82 


1 19.29 


15.90 


19.22 


15.99 


25 


26 


20.21 ; 10.36 


20.13 16.45 


'20.06 


16. .54 


19.99 


16.63 


20 


27 


20.98 1 16.99 


20.91 


17.03 


20.83 


17.17 


20.76 


17.26 


27 


23 


21.76 1 17.62 


'21.63 


17.72 


21.61 


17.81 


21.53 


17.90 


28 


29 


22.54 i 18.25 


22.46 


18.35 


22.33 


18.45 


22.30 


18.54 


29 


30 
31 


23.31 i 18. 8S 


23.23 


18.93 


23.15 


19.03 


23.07 


19.18 


30 
31 


24.09 19.51 


24.01 


19.61 


23.92 


19.72 


23.83 


19.82 


32 


24.87 i 20. 14 


24.78 


20.25 


24.69 


20.35 


24.60 


20.46 


32 


33 


25.65 20.77 


25.55 20.88 


25.46 


20.99 


25.37 


21.10 


33 


34 


26.42 21.40 


26.33 '21.51 


26.24 


21.63 


26.14 


21.74 


34 


35 


27.20 22.03 


27.10 1 22.14 


27.01 


22.26 


26.91 


22.33 


35 


36 


27.98 22.66 


27.83! 22.78 


27.78 


22.90 


27.63 


23.02 


36 


37 


28.75 23. 2S , 


23.65:23.41 


28.55 


23.53 


23.45 


23.66 


37 


38 


29.53 23.91 


29.43 


24.04 


29.32 


24.17 


29.22 124.30 


33 


39 


30.31 24.54 


30.20 


24.68 


30.09 


24.81 


29.93 124.94 


39 


40 
41 


3U09 25.17 
31.86 25.80 1 


30.98 


25.31 


30.86 


25.44 


30.75 125. 58 


40 
41 


31.75 


25.94 


31.64 


26.08 


31.52 


26.22 


42 


32.64 126.43 , 


32.52 26.57 


32.41 


26.72 


32.29 


26.86' 


12 


43 


33.42 127.06 


33.30 


27.21 


3a. 18 


27.35 


33.06 


27.50 


43 


44 


34.19 27.69 


.34.07 


27.84 


33.95 


27.99 


33.83 


28.14 


44 


45 


34.97 28.32 


34.85 


23.47 


34.72 


23.62 


34.60 


28.77 


45 


46 


35.75 ,23.95 


35.62 


29.10 


35.49 


29.26 


35.37 


29.41 


46 


47 


36.53 ,29.58 


36.40 


29.74 


36.27 29.90 1 


36.14 30.05 


47 


48 


37.30 30.21 


37.17 


30.37 


37.04 30.53 


36.90 130.69 


43 


49 


33.03 130.^4 1 


37.95 


31.00 


37.81 131.17 


37.67 131.33 1 


49 


50 
S 

2 


33.86 


31.47 


33.72 


31.64J 


33.53 1 31. 80 


3a.44 


31.9V 


50 

OQ 


Dep. 


Ut. 


Dep. 


L^t. 


Dep. 1 Lat. 


Dep. 


Lat. 


51 Deg. 


501 1 


3eg. 


50i Dog. 


50i Deg. 



TRAVEJISK TABLE. 



151 



s 
? 
51 


39 Deg. 


39i Deg. 


39i Deg. 


391 Deg, 


O 

I- 

s 
n 
a 

"51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

39.35 


Dep. 

32.44 


Lat. 


Dep. 


39.63 


32.10 


39.49 


32.27 


39.21 


32.61 


52 


40.41 


32.72 


40.27 


32.90 


40.12 


33.08 


39.98 


33. 25 


52 


£3 


41.19 


33.35 


41.04 


33.53 


40.90 ' 33.71 


40.75 


33 89 


53 


54 


41.97 


33.98 


41.82 


.34.17 


41.67 134.35 


41.52 


34.53 


54 


65 


42.74 


34 61 


42.59 


34.80 


42.44 


34.98 


42.29 


.35.17 


55 


56 


43.52 1 36.24 


43.37 


35.43 


43.21 


35.02 


43.06 


35.81 


66 


57 


44.30, 35.87 


44.14 


36.06 


43.98 


36.26 


43.82 


36.45 


57 


68 


45.07 36.50 


44.91 


36.70 


44.75 


36.89 


44.59 


37.09 


58 


59 


45.85 


37.13 


45.69 


87.33 


45.53 


37.63 


45.36 


37.73 


59 


60 
61 


48.63 


37.76 
38.39 


46.46 


37.96 


46.30 


38.16 


46.13 


38.37 


60 
61 


47 41 


47.24 


38.60 


47.07 


38.80 


46.90 139.01 


62 


48.18 


39.02 


48.01 


39.23 


47.84 


39.44 


47.67 


39.65 


62 


63 


48.96 


S9.G5 


48.79 


39.86 


48.61 


40.07 


48.44 


40.28 


63 


64 


49.74 


40.28 


49.56 


40.49 


49.38 


40.71 


49.21 


40.92 


64 


65 


50.61 


40.91 


50.34 


41.13 


50.16 


41.35 


49.97 


41.56 


65 


66 


51.29 


41.64 


51.11 


41.76 


50.93 


41.98 


60.74 


42.20 


06 


67 


52.07 


42.16 


61.88 


42.39 


51.70 


42.62 


61.51 


42.84 


67 


68 


52.85 


42.79 


62.66 


43.02 


62.47 


43.25 


52.28 


43.48 


08 


69 


53.52 


43.42 


53.43 


43.66 


63.24 


43.89 


53.05 


44.12 


69 


70 
71 


54.40 


44.05 


54.21 


44.29 


54.01 


44.53 


53.82 


44.76 


70 
71 


55.18 


44.68 


64.98 


44.92 


54.79 


45.16 


54.59 


45.40 


72 


55.95 


45.31 


65.76 


45.55 


55.56 


45.80 


55.36 


46.04 


72 


73 


66.73 


45.94 


56.53 


46.19 


66.33 


46.43 


56.13 


46.68 


73 


74 


67.51 


46.57 


57.31 


46.82 


67.10 


47.07 


56.89 


47.32 


74 


75 


68.29 


47.20 


58,08 


47.45 


57.87 


47.71 


.57.66 


47.06 


75 


76 


.69.06 


47.83 


68.85 


48.09 


68.64 


48.34 


68.43 


48.60 


76 


77 


59.84 


48.46 


59.63 


48.72 


59.42 


48.98 


59.20 


49.24 


77 


78 


60.62 


49.09 


60.40 


49.35 


60.19 


49.61 


59.97 


49.88 


78 


79 


61.39 


49.72 


61.18 


49.98 


60.96 


50.25 


60.74 


50.52 


79 


80 

81 


62.17 


50.35 


61.95 


50.62 


61.73 
62.50 


60.89 


61.51 
62.28 


51.16 


80 
81 


62.95 


50.97 


62.73 


51.25 


51.62 


61.79 


82 


63.73 


51.60 


63.50 


61.88 


63.27 


52.16 


63.04 


62.43 


82 


83 


64.60 


6'J.23 


64.27 


52.51 


64.04 


5^.'>'9 


63.81 


53.07 


83 


84 


65.28 


52.86 


66.05 


63.15 


64.82 


53.43 


64.58 


53.71 


84 


85 


66.06 


53.49 


65.82 


63.78 


65.59 


54.07 


65.35 


64.35 


85 


86 


66.83 


64.12 


66.60 


54.41 


66.36 


64.70 


66.12 


.54.99 


86 


87 


67.61 


54.75 


67.37 


56.05 


67.13 


65.34 


66.89 


65.63 


87 


88 


68.39 


55.38 


68.15 


65.68 


67.90 


66.97 


67.66 


56.27 


88 


89 


69.17 


66.01 


68.92 


.'56.32 


68.67 


56.61 


168.43 


56.91 


89 


90 

91 


69.94 


66.64! 


69.70 


56.94 


69.45 
70.22 


67.25 
57.88 


169.20 


57.65 


90 
'91 


70.72 


57.27 j 


70.47 


.57.58 


i 69.96 


68.19 


92 


71.50 


57.90; 


71.24 


68.21 


70.99 


68.52 


70.73 


68.83 


92 


93 


72.27 


58.53, 


72.02 


68.84 


71.76 


59.16 


71.50 


59.47 


93 


94 


73.05 


59.16 


72.79 


59.47 


72.53 


59.79 


72.27 


60.11 


94 


95 


73.83 


69.79 1 


73.57 


60.11 


73.30 


60.43 


73.04 


60.75 


95 


90 


74.61 


60.411 


74.34 


60.74 


74.08 


61.06 


73.81 


61.39 


9G 


97 


76.38 


61.041 


76.12 


61.37 


74.85 


61.70 


■74.. 58 


62.03 


97 


98 


76.16 


61.671 


75.89 


62.01 


75.62 


62.34 


76.35 


62.66 


98 


99 


76.94 


62.30 


76.66 


62.64 


76.39 


62.97 


76.12 


63.30 


99 


^00 

1 ' 


77.71 


62.93 


77.44 


63.27 


77.16 


63.61 


76.88 


63.94 


100 

6 

1 
1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


51 Deg. 


501 Deg. 


50^ Deg. 


50\ Deg. 



152 



TRAVEKSE TABLE 



o 

B 
o 
n 

1 


40 Deg. 


404 Deg. 


40i Deg. 


40J Deg. 


p 

I 




Lat. 
0.77 


Dep. 

0.64 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. ! 




0.76 


0.65 


0.76 


0.65 


0.76 


0.65 




2 


1.53 


1.29 


1.53 


1.29 


1.52 


1.30 


1.52 


1.31 


2 




3 


2.. 30 


1.93 


2.29 


1.94 


2.28 


1.951 


2.27 


1.96 


3 




4 


3.06 


2.57 


3.05 


2.58 


3.04 


2.60 ; 


3.03 


2.61 


4 




5 


3.83 


3.21 


3.82 


3.23 


3.80 


3.25 ! 


3.79 


3.26 


5 




6 


4.60 


3.86 


4.58 


3.88 


4.56 


3.90 ' 


4.55 


3.92 


6 




7 


5.36 


4.50 


5.34 


4.52 


5.32 


4.55 ! 


5.30 


4.57 


7 




8 


6.13 


5.14 


6.11 


5.17 


6.03 


5.20 : 


6.06 


5.22 


8 




9 


6.89 


5.79 


0.87 


5.82 


6.84 


5.84! 


6.82 


5.87 


9 




10 
11 


7.66 


6.43 


7.63 


6.46 


7.60 


6.49 i 

7.14| 


7.58 


6.53 


10 
11 




8.43 


7.07 


8.40 


7.11 


8.36 


8.33 


7.18 




12 9.19 7.71 


9.16 


7.75 


9.12 


7.79 1 


9.09 


7.83 


12 




13 9.96, 8.36 1 


9.92 


8.40 


9.89 


8.44; 


9.85 


8.49! 


.3 




14 


10.72 


9.00! 


10.69 


9.05 


10.65 


9.09 


10.61 


9.141 


14 




15 


11.49 


9.64 


11.45 


9.69 1 


11.41 


9.74 


11.36 9.79 


15 




16 


12.26 


10.28 


12.21 


10.34! 


12.17 


10.39 


12.12 10.44 


16 




17 


13.02 


10.93 


12.97 


10.98 1 


12.93 


11.04 


12.88 11.10 


17 




18 


13.79 


11.57 


13.74 


11.63 i 


13.69 


11.69 


13.64 


11.75 


18 




19 


14.55 


12.21 


14.50 


12.28 1 


14.45 


12.34 1 


14.39 


12.40 


19 




20 15.32^ 


12.86 


15.26 


12.92 


15.21 


12.99 i 
13.64 1 


15.15 


13.06 


20 
21 




21 


16.09 


13.50 


16.03 


13.57 


15.97 


15.91 


13.71 




22 


16.85 


14.14 


16.79 


14.21 


16.73 


14.29 1 


16.67 


14.35 


22 




23 


17.62 


14.78 


17.55 


14.86 


17.49 


14.94 j 


17.42 


15.01 


23 




24 


18.39 


15.43 


18.32 


15.51 


18.25 


15.59 ! 


18.18 


15.67 


24 




25 


19.15 


16.07 


19.03 


16.15 


19.01 


16.24 


18.94 


16.32 


25 




26 


19.92 


16.71 


19.84 


16.80 


19.77 


16.89 


19.70 


16.97 


26 




27 


20.68 


17.36 


20.61 


17.45 


20.53 


17.54 


20.45 


17.62 


27 




28 


21.45 


18.00 


21.37 


18.09 


21.29 


18.18 


21.21 


18.28 


28 




29 


22.22 


18.64 


22.13 


18.74 


22.05 


18.83 


21.97 


18.93 


29 




30 


22.98 


19.28 


22.90 


19.38 


22.81 


19.48 


22.73 


19.. 08 


30 
31 




31 


23.75 


19.93 


23.66 


20.03 


23.-57 120.13 


23.48 


20.24 




32 


24.51 


20.57 


24.42 


20.68 


24.33 120.78 


24.24 


20.89 


32 




33 


25.28 


21.21 


2i^,i9 


21.32 


25.09 1 21.43 


25.00 


21.54 


33 




34 


26.05 


21.85 


25.95 


21.97 


25.85 122.08 


25.76 


22.19 


34 




35 


26.81 


22.50 


26.71 


22.61 


26.61 22.73 


26.51 


22.85 


35 




30 


27.58 


23.14 


27.48 


23.26 


27.37 23.38 


27.27 


23.50 


36 




37 


28.34 


23.78 


28.24 


23.91 


28.13 24.03 


28.03- 24.15 


37 




38 


29.11 124.43 


29.00 


24.55 


28.90 24.68 


28.79; 24.80 


38 




39 


29.88 125.07 


29.77 


25.20 


29.66 25.33 


29.54 25.46 


39 




40 


30.64 j 25.71 


30.53 


25.84 


30.42 


25.98 


30.30 26.11 


40 




41 


31.41 


26.35 


! 31.29 


26.49 


31.18 


26. G3 


31.06 26.76 


"41 




42 


32.17 


27.00 


32.06 


27.14 


31.94 


27.28 


31.82 27.42 


42 




43 132.94' 27.64 


32.82 


27.78 


32.70 


27.93 


32.58 28.07 


, 43 




44 133.71 i 28.28 


33.58 


28.43 


33.46 


28.58 


33.33 


28.72 


44 




45 


34.47 28.93 


34.35 


29.08 


34.22 


1 29.23 


34.09 


29.37 


45 




46 


35.24 29.57 


35.11 


29.72 


34.98 


29.87 


34.85 


130.03 


! 46 




47 


36.00 


1 30.21 


35.87 


30.37 


35.74 


30.52 


35.61 


i 30.08 


1 -17 




48 


36.77 


[30.85 


36.64 


31.01 


36.50 


31.17 


36.36 


{31.33 


48 




49:37.54 


31.50 


37.40 


31.66 


37.26 


31.82 


37.12 


J31.99 


49 




50^ 


38.30 


32.14 


J8.16_ 


32.31 


38.02 


132.47 


37.88 


32.64 


60 

6 

V 
(S 

1 




c 

ai 

-a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep 


IL.. 




50 Deg. 


49| Deg. 


49h Deg. 


m Deg. 





TRAVERStf TABLE. 



153 



in 

51 


40 Deg, 


40i Deg. 


40^ Dog. 


40| Deg. 


3 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


39.07 


32.78 


38.92 


32.95 


.38.78 


.33.12 


38.64 


33.29 


52 


39.83 


33.42 


39.69 


33.60 


39.54 


33.77 


39.39 


33.94 


52 


53 


40.60 * 34.07 


40.45 


34.^4 


40.30 


34.42 


40.15 


34.60 


53 


54 


41.37 


34.71 


41.21 


34.89 


41.06 


85.07 


40.91 


35.25 


34 


55 


42.13 


35.35 


41.98 


35.. 54 


41.82 


35.72 


41.67 


35.90 


55 


56 


42.90 


36.00 


42.74 


36.18 


42.58 


.36.37 


42.42 


36.55 1 561 


57 


43.66 


.36.64 


43.50 


^6.83 


43.34 


37.02 


43.18 


37.21 


57 


58 


44.43 


37.28 


44.2V 


37.48 


44.10 


37.67 


43.94 


37.86 


68 


59 


45.20 


37.02 


45.03 


38.12 


44.86 


.38.32 


44.70 


38.51 


59 


60 
61 


45.96 


38.57 


45.79 


38.77 


45.62 


38.97 
39.62 


45.45 


39.17 


60 


46.73 


39.21 


46.56 


39.41 


46.38 


46.21 


39.82 


61 


62 


47.49 


39.85 


47.32 


40.06 


47.15 


40.27 


46.97 


40.47 


62 


63 


48.26 


40.50 


48.08 


40.71 


47.91 


40.92 


47.73 


41.12 


63 


64 


49.03 


41.14 


48.85 


41.35 


48.67 


41.56 


48.48 


41.78 


64 


65 


49.79 


41.78 


49.61 


42,00 


49.43 


42.21 


49.24 


42.43 


65 


66 


50.56 


42.42 


50.37 


42.64 


50.19 


42.86 


50.00 


43.08 


66 


67 


51.32 


43.07 


51.14 


43.29 


50.95 


43.51 


50.76 


43.73 


67 


6S 


52.09 


43.71 


51.90 


43.94 


51.71 


44.16 


51.51 


44.39 


68 


69 


52.86 


44.35 


52.66 


44.58 


52.47 


44.81 


52.27 


45.04 


69 


70 
71 


53.62 


45.00 


53.43 


45.23 


53.23 


45.46 


53.03 


45.09 


70 
71 


54.39 


45.64 


54.19 


45.87 


53.99 


46.11 


53.79 


46.35 


72 


55.16 


46.28 


54.95 


46.52 


54.75 


46.76 


54.54 


47.00 


72 


73 


55.92 


46.92 


55.72 


47.17 


55.51 


47.41 


55.30 


47.65 


73 


74 


56 . 69 


47.57 


56.48 


47.81 


56.27 


48.06 


56.06 


48.30 


74 


75 


57.45 


48.21 


57.24 


48.46 


57.03 


48.71 


.56.82 


48.96 


75 


76 


58.22 


48.85 


58.01 


49.11 


57.79 


49.36 


57.57 


49.61 


76 


77 


58.99 


49.49 


58.77 


49.75 


58.55 


50.01 


.58.33 


50.26 


77 


78 


59 . 75 


50.14 


59.53 


50.40 


59.31 


50.66 


59.09 


50.92 


78 


79 


60.52 


50.78 


60.30 


51.04 


60.07 


51.31 


59.85 


51.57 


79 


80 
8i 


61.28 
62.05 


51.42 


61.06 


51.69 


60.83 
61.59 


51.96 
52.61 


60.61 


52.22 


80 
'81 


52.07 


61.82 


52.34 


61.36 


52.87 


82 


62.82 


52.71 


62.59 


52.98 


62.35 


53.25 


62.12 


53.53 


82 


83 


63.58 


53.35 


63.35 


53.63 


63.11 


53.90 


62.88 


54.18 


83 


84 


64.35 


53.99 


64.11 


54.27 


63.87 


54.55 


63.64 


54.83 


84 


85 


65.11 


54.64 


64.87 


54.92 


64.63 


55.20 


64.39 


55.48 85 1 


86 


65.88 


55.28 


65.64 


55.57 


65-39 


55.85 


65.15 


56.14 


86 


87 


66.65 


55.92 


66.40 


56.21 


66.16 


56.50 


65.91 


56.79 


87 


88 


67.41 


56.57 


67.16 


56.86 


66.92 


57.15 


66.67 


57.44 


b8 


89 


68.18 


57.21 


67.93 


57.50 


67.68 


57.80 


67.42 


58.10 


89 


90 
91 


68.94 


57.85 


68.69 


58.15 


68.44 
69.20 


58.45 


68.18 


58.75 


90 


69.71 


58.49 


69.45 


58.80 j 


59.10 


68.94 


69.40 


91 


92 


70.48 


59.14 


70.22 


59.44 


69.96 


59.75 


69.70 


60.05 


92 


93 


71.24 


59.78 


70.98 


60.09 


70.72 


60.40 


70.45 


60.7] 


93 


94 


72.01 


60.42 


71.74 


60.74 


71.48 


61.05 


71.21 


61.36 


94 


95 


72.77 


61.06 


72.51 


61.38 


72.24 


61.70 1 


71.97 


62.01 95 


96 


73.54 


61.71 


73.27 


62.03 


73.00 62.35 


72.73 


62.66 1 96 


97 


74.31 


62.35 


74.03 


62.67 


73.76 63.00 


73.48 


63.32 97 


08 


75.07 


62.99 


74.80 


63.32 


74.52 63.65 


74.24 


63.97! 98 


99 


75.84 


63.64 


75.56 


63.97 


75.28 64.30 


75.00 


64.62 99 


100 

6 

u 

c 

.2 


76.60 


64.28 


76.32 
Dop. 


64.61 


76.04 04.94 


75.76 


65 28 100 


Dep. 


Lat. 


Lat. 

1 


Dep. 1 Lat. 


Dep. 


Lat. 




50 Deg. 


1 
491 Deg. 


49 i Deg. 


49i Deg. 





1.54 



TSAVEBSE TABLE. 



p 

r; 


41 De^. 


4U Deg. 4U Deg. ! 4l| Deg. 


3' 

1 1 


La:. 


Dep. 


Lat. 


D 


?p. Lat. 


Dep. 3 Lat. j Dep. 


^ 


0.75 


0.66 


0.75 


"o" 


C6 0.75 


0.66 0.75 1 67 


~ j 


2 


1.51 


1.31 


1.50 


1 


32 1.50 


1.33 , 1.49 1.33 


2 


3 


2.26 


1.97 


' 2.26 1 


93 2.25 


1.99 I 2.24. 2.00 


3 


4 


3.02 


2.62 


3.01 2 


64 3.00 


2.65 2.98 i 2.66 


4 


c 


3.77 


3. 23 


1 3.76 


3 


3> 3.74 3.31 3.73 1 3.33 


5 


6 


4 53 


3.94 


1 4.5. 




- 4.49 3.98 


4.48 4.00 


6 


7 


5 28 


4.59 


' 5.2'^ 




, 5.24! 4.64 


5.22 4.66 


7 


8 


6.04 


5.25 


' 6.'V 




-~ 5 99i 5.30: 


5.97 1 5.33 


8 


9 


6.79 


5.90 


G.r: 




.: 6.74 1 5.96; 


6.71; 5.99 


9 


10 
11 


7.55 
8.30 


6.56 
7 2*^ 


7.5-: 




7.49! 6.63; 


7.46! 6.66 


10 
11 


8.27 




,' S.24 7.29 'i 8.21 7.32 


12 


9.06 


7!87 


9.0-: 




rl 3.99 7.95;; 8.95 


7.99 


12 


13 


9.81 


8.53 


9.77 




r7 9.74 8.61 ; 9.70 


8.66 


)3 


14 


10.57 


9. IS 


10.53 





-3 10.49 9.28 ■ 10.44 9.32 


14 


15 


11.32 


9.84 


11. 2S 


y 


>? 11.23 9.94 f 11.19 9.99 


15 


16 


12. OS 


10.. 50 


12.03 




': 11.93 10.60 11.94 10.05 


16 


17 


12.83 


11.15 


12.7^ 




,: 12.73 11.26 12.68 11.32 


17 


18 


13. 5S 


11.81 


13.. = 3 




-' 13.43 11.93 ; 13.43 11.99 


13 


19 


14.34 


12.47 


14.-:- 


:•; 


ry 14.23 12.59 ; 14.18; 12.65 


19 


20 


15.09 13.12 


15.04: 


■ Q 


: 14.93 13.25 [ 14.92 1 13.32 


20 


21 


15.85 13. 7S 


15.79 


13. 


So 15.73 13.91: 15.67 13.98 


21 


no 


16.60 14.43 


16.54 


14. 


51 16.48 14.58 16.41 14.65 


22 


23 

24 


17.36 
13.11 


15.09 


17.29 


15. 


16 17.23 


15.24; 17.16 15.32 
15.90 17.91 15.98 


23 
24 


15,: ' 


1 ■* . ' -i 


: " 


^; 17.97 


25 


IS. 87 le.:: 


> . - - 




4^ IS. 72 16. .57 18.65 16.65 


25 


26 


19.62 17.. 6 


1 -^ . J •' 


: ^ , 


^ 19.47 17.23 19.40.17.31 


26 


27 


20. 3S 17.71 


20.3^ 




- 20.22 17.89 ,20.14 17.98 


27 


2S 


21.13 IS. 37 


21. Or 


'. i . 


^' CO. 97 lS..55i 20.89 18.64 


28 


29 


21. S9 


19.03 


'2\S : 




:: •:i.72 19.22 21. at 19.31 


29 


30 
31 


22.64 


19.63 


2i.5- 




^^ •:2.47 


19.33 22.33 19. 9S 
•::'.-4 •:3.I3 20.64 


30 
"31 


23.40 


20.34 


^.3^ 




1- C:'.-C 


32 


24.15 


20.99 


24.0: 


: : , 


: b'." •::.-:: C3.S7 21.31 


32 


33 


24.91 


21.65 


24. S 


', : , 


: 14-; , .-: :4. 62 21.97 


3S 


34 


25.66 22.31 


25, c"^ 




4: :^l ::..53 25.37 22.64 


34 


35 


•2^.41 22.96 


23.3: 


■:: . 


^ :■ .: 1 19 26.11 23.31 


35 


S6 


27.17 23.62 


27 .''T 


■^ : . 


^^ i'.,' i.<5 26.36 23.97 


36 


37- 


27.92 24.27 


27. SC 


; ;. . 


. CT.Tl ':4.52 27.60 24.64 


37 


3S 


2S.6^ 24.93 


r> ^ ."7 




:S.4o '25 AS 2S. 35 25.30 


38 


39 


29.43 25.59 


29 is-: 


Co . 


71 -ZB.^l •;'.^4 ':9. 10 (25.97 


39 


40 


30.19 26.24 


30.07 


26. 


37 29. P5 •: .^ Cy. 34 26.64 


40 


41 


30.94 26.90 


30.33 


27 . 


03 30.71 - .:: 30.59 27.30 


41 


42 


31.70 27.55 


31.53 


27. 


69 31.4-3 •:.-.-: 81.33-27.97 


42 


43 


32.45 23.21 


32.33 


23 . 


35 32.2: :-.: ^C.OS 2-S.03 


43 


44 


.33.21 2S.S7 


33. 0> 


"3^ 


'•: -^CP' - 3:. 33 29.30 


44 


45 


33.96 29.52 


33.-? 


; r 


^ : - -1^1 53. 57. 29. 97 


45 


46 


34.72 30.13 


34..= ^ 




: i.:^ : ^- 34.32 30.63 


46 


47 


35.47 30. S3 


35.3^ 




'■.-, :: ?o.06' 31.30 


47 


48 


36.23 31.49 


36. 0> 




: - 35.31 !31 96 


48 


49 


38. 9S 32.15 


35. S. 


' -l 


: :^ 35.56 32.63 


49 


50 

1 


37.74 32.80 
Dep. '. Lat. 


37.5. 




r~ 3^.45 33.13 


37.30 33.29 
Dep. 1 Lat. 


50 

' i 

c 
ti 

.J 


Dep 


L 


-:, Dep. 


Lat. 
Dej. 




491 


>-■ 


48.' Der 


! 48r 


m 


Deg. 



TRAVERSE TABLE. 



155 



41 Deg. 



4U Deg. 



Lat Dep. | Lat. , Dep. 



52 ; 39 . 



57 43 

53 '43 
5e 144 

61 I 46 

62 146 

63 147 

64 [48 

65 I 49 

66 !49 

67 : 50 

68 51 



49 33.46 

24 34.12 
00; 31.77 
75 35.43 
51 136.0S 
26 36.74 
02' 37.40 
77 38.05 
53 3S.71 

25 39.36 



69 
70 



40 . 02 
40.68 
41.33 
41.99 

06 j 42 . 64 
81 '43.30 
57 43. 9G 
32 44.61 

07 45.27 
83 45.92 



71 53, 

72 i 54, 
73; 55, 
74155, 

75 ■ 56 , 

76 I 57, 

77 58, 

78 I 53, 

79 1 59 , 

80 I 60, 



58 46.58 
.34 47.24 
09 47.89 
85 48.55 
60 49.20 
36,49.86 
11 ! 50.52 
87 51.17 
62 51.83 
38 52.48 



81 ; 61. 
82^61. 
83 162. 
84i63. 

85 64. 

86 64. 

87 65. 
83 66. 
89 67. 

_90 6]_. 

91 63. 

92 I 69. 
93, 70. 
94 70, 
95 '71. 

96 172. 

97 73. 

93 73. 
99 , 74. 



13 53.14 



53.80 
54.45 
55.11 



15 55.76 



90 56.42 

66 57.08 

41 57.73 

17 58.39 

92 59.05 



63 59.70 

43 60.36 

19 61.01 

94 61.67 

70 62.33 

45 62.98 

21 63.64 

96 64.29 

72 64.95 



100 • 75.47: 65.61 



38.34 

39.10 
39.85 
40.60 
41.35 
42.10 
42.85 
43.61 
44.36 
45.11 
45.86 
46.61 
47.37 
48.12 
48.87 
49.62 
50.37 
51.13 
51.88 
52.63 
53.38 
54.13 
54.88 
55.64 
56.39 
57.14 
57.89 
.58.64 
59.40 
60.15 



33. 
34. 
34. 
35. 
36. 
36. 
37. 
38. 
33, 
39. 
40, 
40, 
41, 
42, 
42, 
43, 
44, 
44, 
45, 
46, 



41i Deg. 



Lat. 



63 

29 
95 
60 
26 
92 
58 
24 
90 
56 
22 
88 
54 
20 
86 
52 
IS 
S4 
49 



33.20 
38.95 
39.69 
40.44 
41.19 
41.94 
42.69 
43.44 
44.19 
44.94 
45.69 
46.44 
47.18 
47.93 
48.68 
49.43 

50! 93 
51.68 
52.43 



Dep. 



33.79 
.34.46 
35.12 
35 . 78 
36.4-4 
37.11 
37.77 
33.43 
39.09 
39.76 
40.42 
41.08 
41.75 
42.41 
43.07 
43.73 
44.40 
45.06 
45.72 
46.38 



411 Deg. 



60.90 
61.65 
62.40 
63.15 
63.91 
64.66 
65.41 I 57, 
66.16 153, 
66.91 1 53, 

67.67 1 59, 
68.42 
69.17 
69.92 
70.67 
71.43 
72.18 
72.93 ' 63, 

73.68 '64, 
74.43 165, 
75.18 



65 



i 53.18 

i| 53.92 

154.67 

55.42 

I 56.17 

: 56.92 

' 57.67 

! 53.42 

I 59.17 

! 59.92 

i 60.67 

! 61.41 

; 62.16 

' 62.91 

' 63.66 

: 64.41 

65.16 

65.91 

66.66 

67.41 

• 68.15 

68.90 

69.65 

70.40 

71.15 

; 71.90 

72.65 

73.40 

74.15 

74.90 



47.05 
47.71 
48.37 
49.03 
49.70 
50.36 
51.02 
51 .68 
52.35 
53.01 
53.67 
54.33 
55 . 00 
55.66 
56.32 
56.99 
57.65 
53.31 
53.97 
59.64 
60.30 
60.96 
61.62 
62.29 
62.95 
63.61 
64.27 
64.94 
65.60 
66.26 



Lat. I Dep. 3 



I » 



33.05 I 33.96 ' 51 

38.79 34.63 52 

39.. 54 35.29 53 

40.29 35.96 ' .54 

41.03 36.62 55 

41.73 37.29 56 

42.53 37.96 57 

43.27 33.62 

44.02 39.29 

44.76 39.95 



45.51 
46.26 
47.00 
47.75 
48.49 
49.24 
49.99 
50.73 
51.43 

5-:2.22 

52.97 
53.72 
54.46 
55.21 
55.95 
56.70 
57.45 
53.19 
58.94 
59.68 



40 . 62 
41.28 
41.95 

42 . 62 
43.28 

43 . 95 
44.61 
45.28 
45.95 
46.61 



47.28 
47.94 
48.61 
49.28 
49.94 
50.61 
51.27 
51.94 
52.60 
53.27 



60.43 
61.18 
61.92 
62.67 
63.41 
64.16 
64.91 
65.65 
66.40 
67.15 
67.89 
68 . 64 
69.38 
70.13 
70.88 
71.62 
72.37 
73.11 
73.88 
74.61 



53.94 
54.60 
55.27 
55.93 
56.60 
57.27 
57.93 
58.60 
59.26 
59.93 
60.60 
61.26 
61.93 
62 . 59 
63.26 
63.92 
64.59 
65.26 
65.92 



66.59 lOi^ 



Dep. I Lat. ;, Dep. | Lat. i Dep. j Lat. : D^p. I Lat. 



49 Deg. 



48| De^ 



48^ Deg. 



48i Deg. 



156 



TRAVERSE TABLE. 



5 

a 
n 
9 


42 Deg. 


424 Dog. 


42h Deg. 


— — 
42| Deg 


' T 


Lat. 


Dep. 1 
0.67 


Lat. 

0.74 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 0.74 


0.67 


0.74 


0.68 


0.73 


0.68 


2 


1.49 


1.34 


1.48 


1.34 


1.47 


1.35 


1.47 


1.36 


2 


3 


2.23 


2.01 


2.22 


2.02 


2.21 


2.03 


2.20 


2.04 


3 


4 


2.97 


2.68 


2.96 


2.69 


2.95 


2.70 


2.94 


2.73 


4 


5 


3.72 


3.35 


3.70 


3.36 


3.69 


3.38 


3.67 


3.39 


5 


6 


4.46 


4.01 


4.44 


4.03 


4.42 


4.05 


4.41 


4.07 


6 


7 


5.20 


4.68 


5.18 


4.71 


5.16 


4.73 


5.14 


4.75 


7 


8 


5.95 


5.35 


5.93 


5.38 


5.90 


5.40 


5.87 


5.43 


8 


9 


6.69 


6.03 


6.66 


6.05 


6.64 


6.08 


6.61 


6.11 


9 


10 

if 


7.43 

8.17 


6.69 
7'. 3 6 


7.40 


6.72 


7.37 


6.76 
7.43 


7.34 


6.79 


10 


8.14 


7.40 


8.11 


8.08 


7.47 


11 


12 


8.93 


8.03 


8.88 


8.07 


8.85 


8.11 


8.81 


8.15 


12 


13 


9.66 


8.70 


9.63 


8.74 


9.58 


8.78 


9.. 55 


8.82 


13 


14 


10.40 


9.37 


10.36 


9.41 


10.33 


9.46 1 


10.28 


9.50 


14 


15 


11.15 


10.04 


11.10 


10.09 


11.06 


10.13' 


11.01 


10.13 


15 


16 


11.89 


10.71 


11.84 


10.76 


11.80 


10.81 i 


11.75 


10.86 


10 


17 


12.63 


11.38 


13.58 


11.43 


12.53 


11.48 


12.48 


11.54 


17 


18 


13.38 


13.04 


13.33 


12.10 


13.27 


12.16 1 


13.22 


13.32 


13 


19 


14.12 


13.71 


14.06 


12.77 


14.01 


13.84! 


13.95 


13.90 


19 


20 
21 


14.86 


13.38 


14.80 


13.45 


14.75 


13.51 1 


14.69 


13. 5S 


20 


15.61 


14.05 


15.54 


14.12 


15.48 


14.19; 


15.42 


14.25 


21 


22 


16.35 


14.73 


16.28 


14.79 


16.22 


14.86 1 


16.16 


14.93 


22 


23 


17.09 


15.39 


17.02 


15.40 


16.96 


15.54 1 


16.89 


15.61 


23 


24 


17.84 


16.06 


17.77 


16.14 


17.69 


16.21 1 


17.62 


16.29 


24 


25 


18.58 


16.73 


18.51 


16.81 


18.43 


16.89 1 


18.36 


16.97 


25 


26 


19.33 


17.40 


19.25 


17.48 


19.17 


17.57 1 


19.09 


17.65 


26 


27 


20.06 


18.07 


19.99 


18.15 


19.91 


18.24 1 


19.83 


18.. 33 


27 


28 


20.81 


18.74 


20.73 


18.83 


20.64 


18.92 1 


20.56 


19.01 


28 


29 


21.55 


19.40 


21.47 


19.50 


21.38 


19.59 


21.30 


19.69 


29 


30 


22.29 


20.07 


22.21 


20.17 


22.12 


30.37 


22.03 


20.36 


30 
31 


31 


23.04 


20.74 


22.95 


20.84 


23.86 


20.94 


22.76 


21.04 


32 


23.78 


21.41 


23.69 


21.53 


23.59 


21.62 


23.50! 21.72 


32 


33 


24.52 


23.08 


24.43 


22.19 


24.33 


22.29 


24.23 


22.40 


33 


34 


25.27 


22.75 


25.17 


22.86 


25.07 


22.97 


24.97 


23.08 


34 


35 


26.01 


23.42 


25.91 


23.53 


25.80 


23.65 


25.70 


23 . 76 


35 


36 


26.75 


24.09 


26.65 


24.21 


26.54 


24.32 


26.44 


24.44 


36 


37 


27 50 


24.76 


27.39 


24.88 


27.28 


25.00 


27.17 


25.12 


37 


38 


28.24 


25.43 


28.13 


25.. 55 


28.03 


25.07 


27.90 


25.79 


38 


39 


28.98 


26.10 


28.87 


26.23 


28.75 


26.35 


28.64 


26.47 


39 


40 


29.73 


26.77 


29.61 


26.89 


29.49 


27.02 


29.37 1 27.15 


40 


41 


30.47 


27.43 


30.35 


27.57 


30.23 


27.70 


130.11 27.83 


41 


42 


31.21 


28.10 


31.09 


28.24 


30.97 


28.37 


130.84 28.51 


42 


43 


31.96 


28.77 


31.83 


28.91 


31.70 


29.05 


131.58 29.19 


43 


44 


33.70 


29.44 


32.57 


29.58 


32.44 


29.73 


132.31 129.87 


44 


45 


33.44 


30.11 


33.31 


30.26 


33.18 


39.40 


133.04 


30.. 55 


45 


46 134.18 


30.78 


34.05 


30.93 


33.91 


31.08 


1 33.78 


31.22 


46 


47 


34.93 


31.45 


34.79 


31. GO 


34.65 


31.75 


134.51 


31.90 


47 


48 


35.67 


33.12 


35.53 


32.27 


35.39 


32.43 


35.25 


32.. 58 


48 


49 


36.41 


32.79 


36.27 


32.95 


36.13 


33.10 


.35.98 


33.26 


49 


50 

1 


37.16 
Dop. 


33.46 


37.01 


33.62 


36.86 


33.78^ 


.36.72 
Dep. 


33.94 
Lat. 


.50 

o 
c 
2 

.2 

e 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


48 Deg. 


47| Deg. 


47i Deg. 


47i Deg. 



TBAV3SRSE TABLE. 



157 



"5i 


42 Deg. 

1 


42i De^. 


42i Deg. 

1 


42| Deg. 


s 
? 
51 


Lat 


Dep. 
34.13 


Lat. 


Dep. 


Lat. 


De,. 


Lat. 


Dep. 


37.90 


37.75 


34.29 


37.60 


34.46 


37.45 


34.62 


53 


3S.64 


34.79 


38.49 


34.96 


38.34 


35.13 


38.18 


35.30 


32 


53 


39.39 


35.46 


39.23 


35.64 


39.08 


35.81 


38.92 


35.93 


63 


54 


40.13 


36.13 


39.97 


36.31 


39.81 


36.48 


39.65 


36.66 


54 


55 


40.87 


36.80 


40.71 


36.93 


40 55 


37.16 


40.39 


37.33 


55 


66 


41.62 


37.47 


41.45 


37.65 


41.29 


37.83 


41.12 


38.01 


56 


57 


42.36 


38.14 


42.19 


38.32 


42.02 


38.51 


41.86 


38.69 


57 


58 


43.10 


38.81 


42.93 


39.00 


42.76 


39.18 


42.59 


39.37 


53 


59 


43.85 


39.48 


43.67 


39.67 


43.50 


39.86 


43.32 


40.05 


59 


60 
"61 


44.59 


40.15 


44.41 


40.34 


44.24 


40.541 


44.06 


40.73 


60 
61 


45.33 


40.82 


45.15 


41.01 


44.97 


41.21 


44.79 


41.41 


62 


46.07 


41.49 


45.89 


41.69 


45.71 


41.89 


45.53 


42.09 


62 


63 


46.82 


42.16 


46.63 


42.36 


46.45 


42.56 


46.26 


42.76 


63 


64 


47.56 


42.82 


47.37 


43.03 


47.19 


43.24 


47.00 


43.44 


64 


65 


48.30 


43.49 


48.11 


43.70 


47.92 


43.91 


47.73 


44.12 


65 


66 


49.05 


44.16 


48.85 


44.38 


48.66 


44.59 


48.47 


44.80 


66 


67 


49.79 


44.83 


49.59 


45.05 


49.40 


45.26 


49.20 


45.48 


67 


68 


50.53 


45.50 


50.33 


45.72 


50.13 


45.94 


49.93 


46.16 


68 


69 


51.28 


46.17 


51.07 


46.39 


50.87 


46.62 


50.67 


46.84 


69 


70 
"71 


52.02 


46.84 


51.82 
52.56 


47.07 


51.61 


47.29 


51.40 


47.52 


70 
71 


52.76 


47.51 


47.74 


52.35 


47.97 


52.14 


48.19 


72 


.53.51 


48.18 


53.30 


48.41 


.53.08 


48.64 


,52.87 


48.87 


72 


73 


54.25 


48.85 


54.04 


49.08 


53.82 


49.82 


53.61 


49.55 


73 


74 


54.99 


49.52 


.54.78 


49.76 


54.56 


49.99 


54.34 


.^0.23 


74 


75 


55.74 


50.18 


55.52 


50.43 


55.30 


50.67 


155.07 


50.91 


75 


76 


56.48 


.50.85 


56.26 


51.10 


56.03 


51.34 


155.81 


51.59 


76 


77 


57.23 


51.52 


57.00 


51.77 


56.77 


.52.02 


156.54 


52.27 


77 


78 


57.97 


52.19 


57.74 


52.44 


57.51 


52.70 


57.28 


52.95 


78 


79 


58.71 


52.86 


58.48 


53.12 


58.24 


53.37 


58.01 


53.63 


79 


80 
81 


59.45 


,53.53 


59.22 


53.79 


58.98 


54.05 


58.75 


54.30 


80 
81 


60.19 


54.20 


59.96 


54.46 


59.72 


54.72 


159.48 


54.98 


82 


60.94 


54.87 


60.70 


55.13 


60.46 


55.40 


! 60.21 


55.66 


82 


83 


61.68 


55.54 


61.44 


55.81 


61.19 


56.07 


160.95 


56.34 


83 


84 


62.42 


56.21 


62.18 


56.48 


61.93 


56.75 


161.68 


57.02 


84 


85 


63.17 


56.88 


62.92 


57.15 


62.67 


57.43 


162.42 


57.70 


85 


86 


63.91 


57.55 


63.66 


57.82 


63.41 


58.10 


63.15 


58.38 


86 


87 


?4.65 


58.21 


64.40 


58.50 


64.14 


58.78 


63.89 


59.06 


87 


88 


65.40 


58.88 


65.14 


59.17 


64.88 


59.45 


64.62 


59.73 


88 


89 


66.14 


59.55 


65.88 


59.84 


65.62 


60.13 


'65.35 


60.41 


89 


90 
91 


66.88 


60.22 
60.89 


66.62 


60.51 


66.35 


60.80 


66.09 


61.09 


90 
91 


67.63 


67.36 


61.19 


67.09 161.48 


166.82 


61.77 


92 


68.37 


61.56 


68.10 


61.86 


67.83 62.15 


167.56 


62.45 


92 


93 


69.11 


62.23 


68.84 


62.53 


68.57 63.83 


i 68.29 


63.13 


93 


94 


69.86 


62.90 


69.58 


63.20 


69.30 163.51 


69.03 


63.81 


94 


95 


70.60 


63.57 


70.32 


63.87 


70.04 164.18 


1 69.76 


64.49 


95 


96 


71.34 


64.24 


71.06 


64.55 


70.78 ' 64.86 


70.49 


65.16 


9G 


97 


72.08 


64.91 


71.80 


65.22 


71.52 ; 65.53 


171.23 


65.84 


97 


98 


72.83 


65.57 


72.54 


65.89 


72.25 


66.21 


71.96 


66 52 


98 


99 


73.57 


66.24 


73.28 


66.56 


72. 99 


66.88 


72.70 


67.20 


99 


100 

6 
u 
a 
S 
.2 
O 


74.31 


66.91 


74.02 


67.24 


73.73 


67.56 


173.43 


67.88 


100 

6 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


48 Deg. 


471 Deg. 


-■ 
47^ Deg. 


1 

47i Deg. 



158 



TRAVERSE TABLE. 



c 

DO 

1 

P 
1 


43 Deg. 


A2\ Deg. 


43i Deg. 


431 Deg. 


5- 

g 
p 

1 


Lat. 


Dep. 


Lat. 
0.73 


Dep. 
0.69 


Lat. 


Dep. 


Lat. 
0.72 


Dep. 


0.73 


0.68 


0.73 


0.69 


0.69 


2 


1.46 


1.36 


1.46 


1.37 


1.45 


1.38 


1.44 1.38 


2 


3 


2.19 


2.05 


2.19 


2.06 


2.18 


2.07 


2.17 2,07 


8 


4 


2.93 


2.73 


2.91 


2.74 


2.90 


2.75 


2.89 1 2 77 


4 


5 


3.66 


3.41 


3.64 


3.43 


3.63 


3.44 


3.61 3 46 


5 


6 


4.39 


4.09 


4.37 


4.11 


4.35 


4.13 


4.33 4.15 


6 


7 


5.12 


4.77 


5.10 


4.80 


5.08 


4.82 


5.06 4.84 


7 


8 


5.85 


5.46 


5.83 


5.48 


5.80 


5.51 


5.78 5.53 


8 


9 


6.58 


6.14 


6.56 


6.17 


6.53 


6.20 


6.50 6.22 9 


10 


7.31 


6.82 


7.28 


6.85 


7.25 


6.88 


7.22 6 92| 10 


11 


8.04 


7.. 50 


8.01 


7.54 


7.98 


7.57 


7.95 


7.61 ! 11 


12 


8,78 


8.18 


8.74 


8.22 


8.70 


8.26 


8.67 


8.30 1 12 


13 


9.51 


8.87 


9.47 


8.91 


9.43 


8.95 


9.39 


8.99' 13 


14 


10.24 1 9.55 


10.20 


9.59 


10.16 


9.04 


10.11 


9.68! 14 


15 


10.97 1 10.23 


10.93 


10.28 


10.88 


10.33 


10.84 10.37 


15 


16 


1 1 . 70 


10.91 


11.65 


10.96 


11.61 


11.01 


11.56! 11.06 


16 


17 


12.43 


11.59 


12.33 


11.65 


12.33 


11.70 


12.28! 11.76 


17 


18 


13.16 


12.28 


13.11 


12.33 


13.06 


12.39 


13.00! 12.45 


18 


19 


13.90 


12.98 


13.84 


13.02 


13.78 


13.08 


13.72. 13.14 


19 


20 


14.63 


13.54 


14.57 


13.70 


14.51 


J3.77 


14.45 1 13.83 


20 


21 


15.36 


14.32 


15.30 


14.39 


15.23 


14.46 


15.17 14.. 52 


21 


22 


16.09 


15.00 


1tj.02 


15.07 


15.96 


15.14 


15.89 15.21 


22 


23 


16.82 


15.69 


16.75 


15.76 


16.68 


15.83 


16.61 15.90 23 


24 


17.55 


16.37 


17.48 


10.44 


17,41 


16.52 


17.34 16.60 24 


25 


18.28 


17.05 


18.21 


17.13 


18.13 


17.21 


18.06 17.29! 25 


26 


19.02 


17.73 


18.94 


17.81 


18.86 


17.90 


18.78 1 17.93 1 26 


27 


19.75 


18.41 


19.67 


18 50 


19-53 


18.59 


19.50! 18.67 27 


28 


20.48 19.10 


20.39 


19.19 


20.31 


19.27 


20.23; 19.36 1 28 


29 


21.21 19.78 


21.12 


19.87 


21.04 


19.96 


20.95 '20.05 29 


30 


21.94! 20.46 


21.85 


20.56 


21.76 1 20.65 


21.67 120.75 


30 


:ii 


22.67 


21.14 


22.58 


21.24 


22.49 


21.34 


22.39; 21.44 


"31 


32 23.40 


21.82 


23 31 


21.93 


23.21 


22.03 


23.12 22.13 1 32 1 


33 


24.13 


22.51 


24.04 


22.61 


23.94 22.72 


23.84 22.82 


33 


34 


24.87 


23.19 


24. 7C. 


23.30 


24.66] 23.40 


24.66 23.51 


34 


35 


25.60 


23.87 


25.49 


23.98 


25.39 24.09 


25.28 24.20 


35 


36 


26.33 


24.55 


26.22 


24.67 


26.11 1 24.78 


26.01 24.89 


36 


37 


27.06 


25.23 


26.95 


25.35 


26.841 25.47 


26.73 i 25.59 


37 


3S 


27.79 


25.92 


27.68 


26.04 


27.56 


26.16 


27.45 i 26.23 t 38 | 


39 


28.52 


26.60 


28.41 


26.72 


28.29 


26.85 


28.171 26.97! 39) 


40 
41 


29.25 
29.99 


27.28 


29.13 


27.41 


29.01 


27.53 


28.89 27.66 


40 


27.96 


29.86 


28.09 


29.74 


23.22 


29.62 i 28.35 


41 


42 


30.72 


28.64 


30.59 


28.78 


30.47 


23.91 


30.34 


29.04; 42 


43 


31.45 


29.33 


31.32 


29.46 


31.19 


29.60 


31.06 


29 . 74 i 43 


44 


32.18 


30.01 


32.05 


50.15 


31.92 


30.29 


31.78 


30.43 1 44 


45 


32.91 


30.69 


32.78 


30.83 


32.64 


30.93 1 


.32.51 31.12 j 45 


46 


33.64 


31.37 


33.51 


31.52 


33.37 31.66 


33.23 31.81 , 46 


47 


34.37 


32.05 


34.23 


32 . 20 


34.09 32.35 


33.95 32.50' 47 


48 


35.10 


32.74 


34.96 


32.89 


34.82 1 33.04 


3-^.67 ??.19 48 


49 


35.84 


33.42 


35.69 


33.57 


35.54 33.73 


35.40 3.1 88 1 49 


50 


36.. 57 


34.10 


36.42 


34.26 


30.27 


34,42 


3ti.l2 


l^..i9 1 60 J 


i4 
'oo 

Q 


Dep. 


Lat. 


Dep. 


Lat. 

1 


Dep. 


Lat. 


Dep. 


Lat. 


i 


47 Deg. 


46f Deg. 


46 i Deg. 


46^ Deg 



TRAVERSE TABLE. 



1B9 





43Deg. 


43| Deg. 


431 Deg. 


43| Deg. 




i 


Lat. 


Dep. 


Lat. 1 Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


,37.30 


34.73 


37.15 .34.94 


36.99 


35.11 1 


36.84 


35.27 


51 


52 


33.03 


35.46 


37.88 '35.63 


37.72 


35.79 1 


37.56 


35.96 


52 


53 


38.76 


36.15 


38.60 '36.31 


38.44 


36.48 1 


33.29 


36.65 


53 


54 


39.49 


36.83 


39.33 37.00 


39.17 


37.17! 


39.01 


37.34 


54 


55 


40.22 ' 37.51 


40.06 137.69 


39.90 


37.86 


39.73 


38.03 


55 


56 


40.96:38.19 


40.79 38.37 


40.62 


38.55 


40.45 


38.72 


56 


57 41.69 


38.87, 


41.. 52 


39.06 


41.35 


39.24 


41.17 39.42 


57 


58 


42.42 


39.56 


42.25 


39.74 


42.07 


39.92 


41.90 40.11 


68 


69 


43.15 


40.24 


42.97 


40.43 


42.80 


40.61 


42.62 


40.80 


59 


60 
61 


43.88 


40.92 


43.70 
44.43 


41.11 
41.80 


43.52 


41.30 


43.34 


41.49 


60 
61 


44.61 


41.60 


44.25 


41.99 


44.06 


42.18 


62 


45.34 


42.28 


45.16 


42.48 


44.97 


42.68 


44.79 


42.87 


62 


63 


46.08 


42.97 


45.89 43.17 


45.70 


43.37 


45.51 


43.. 57 


63 


64 


46.81 


43.65 


46.62 43.85 


46.42 


44.05 


46.23 


44.20 


64 


65 


47.54 


44.33 


47.34 44.54 


47.15 


44.74 


46.95 


44.95 


65 


66 


48.27 


45.01 


43.07 45.22 


47.87 


45.43 


47.68 


45.64 


66 


67 


49.00 


45.69 


48.80 45.91 


48.60 


46.12 


48.40 


46.33 


67 


68 


49.73 


46.38 1 


49.53 46.59 


49.33 


46.81 


49.12 


47.02 


68 


69 


50.46 


47.06 


50.26 47.28 


50.05 


47.50 


49.84 


47.71 


69 


70 
71 


51.19 


47.74 1 


50.99 47.96 


50.78 48.18 


50.57 


48.41 
49.10 


70 

71 


51.93 


48.42 


51.71 148.65 ti 51.50 


48.87 


51.29 


72 


52.66 


49.10 


52.44^49.33 


52.23 


49.56 


52.01 


49.79 


72 


73 


53.39 


49.79' 


53.17 150.02 


.52.95 


50.25 


52.73 


50.48 


73 


74 


54.12 


50.47 


53.90 150.70 


53.68 


50.94 


53.45 


51.17 


74 


75 


54.85 


51.15 


54.63 


51.39 


54.40 


51.63 


54.18 


51.86 


75 


76 


55.58 


51.83 


55.36 


52.07 


55.13 


52.31 


54.90 


52.55 


76 


77 


56.31 


52.51 


56.08 


52.76 


55.85 


53.00 


55.62 


53.25 


77 


78 


57.05 


53.20 


56.81 


53.44 


56.58 


53.69 


156.34 


53.94 


78 


79 


57.78 


53.88 


57.54 


54.13 


57.30 


54.38 


157.07 


54.63 


79 


80 


58.51 


54.56 


58.27 


54.81 


58.03 


.55.07 


157.79 


55.32 


80 
81 


81 


59.24 


55.24 


59.00 155.50 


58.76 


55.76 


158.51 


56.01 


82 59.97 


55.92 


59.73 |50.18 


59.48 


56.45 


159.23 


56.70 


82 


83 60.70 


.50.61 


60.45 


50.87 


60.21 


57.13 


1 59.96 


57.40 


83 


84 61.43 


57.29 


61.18 


57.56 


60.93 


57.82 


160.68 


58.09 


84 


85 62.17 


57.97 


01.91 


58.24 


61.60 


58.51 


161.40 


58.78 


85 


88 62.90 


58.65 


62.64 


58.93 


62.38 


59.20 


162.12 


59.47 


86 


87 03.63 


59.33 


63.37 


59.61 


63.11 


59.89 


62.85 1 60.16 


87 


88 64.36 


60.02 


64.10 


60.30 


63.83 


60.58 


63.57 


60.85 


88 


89 65.09 


60.70 


64.82 


60.98 


64.56 


61.26 


64.29 


61.54 


89 


90 


65.82 


61.38 


65.55 161.67 


65.28 


61.95 


165.01 


62.24 


90 
91 


91 


66.55 162.06 


66.28 162.35 


66.01 


62.64 


65.74 


62.93 


92 167.28 ; 02.74 


67.01 


63.04 


66.73! 63.33 


66.46 


63.62 


92 


93 j 68.02 63.4? 


67.74 


63.72 


67.46 1 64.02 


67.18 


64.31 


93 


94 i 68.75 64.11 


f 68.47 


64.41 


68.19 '64.71 


67.90 


65.00 


94 


95 169.48 64.79 


69.20 


65.09 


! 68.91 165.39 


68.62 


65.69 


95 


96 70.21 65.47 


69.92 


65.78 


69.64 


66.08 


69.35 


66.39 


96 


97 70.94 66.15 


70.65 


60.46 


1 70.36 


66.77 


70.07 


67.08 


97 


98 171.67 66.84 


71.37 


67.15 


171.09 


67.46 


170.79 


67.77 


98 


99 i 72.40 ; 67.52 


72.11 


67.83 


71.81 


68.15 


171.51 


68.46 


99 


100 


73.14 


68.20 


72.84 
Dep. 


68.52 


72.54 


68.84 


72.24 


69.15 


100 

1 


I 


Dep. 


Lat. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


47 Deg. 


461 Deg. 

1 


461 Deg. 


46J Deg. 



160 



TRAVERSi:: TABLE. 



~1 


44Deg. 


U\ Deg. 


44 i Deg. 


44J Deg. 


.45 Deg. 


C 
0; 

p 

3 

3 

I 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
0.71 


Dep. 

"oTto 


Lat. 


Dep. 


Lat. 


Dep. 


0.72 


0.69 


0.72 


0.70 


0.71 


0.71 


0.71 


0.71 


"Z 


1.44 


1.39 


1.43 


1.40 


1.43 


1.40 


1.42 


1.41| 


1.41 


1.41 


a 


a 


2.16 


2.08 


2.15 


2.09 


2.14 


2.10 


2.13 


2.11 


2.12 


2.12 


a 


4 


2.88 


2.78 


2.87 


2.79 


2.85 


2.80 


2.84 


2.82! 


2.83 


2. 83 4 i 


£ 


3.60 


3.47 


3.58 


3.49 


3.57 


3 50 


3.55 


3..52i 


3.. 54 


3.64 





ti 


4.32 


4.17 


4.30 


4.19 


4.28 


4.21 


4.26 


4.22! 


4.24 


4.24 


€ 


7 


5.04 


4.86 


5.01 


4.88 


4.99 


4.91 


4.97 


4.93 


4.95 


4.95 


1 


« 


5.75 


5.56 


6.73 


5.58 


5.71 


5.61 


6.68 


6.63 


5.66 


5.66 


8 


9* 6.47 


6.25 


6.45 


6.28 


0.42 


6.31 


6.39 


6.34 


6.36 


6.36 


9 


10 
11 


7.19 
7.91 


6.95 


7.16 

7.88 


6.98 


7.13 


7.01 


7.10 


7.04 


7.07 


7.071 10 
7.78ill 


7.64 


7.68 


7.85 


7.71 


7.81 


7.74 


7.78 


12 


8.63 


8.34 


8.60 


8.37 


8.56 


8.41 


8.52 


8.45! 


8.49 


8.49 


12 


13 


9.35 


9.03 


9.31 


9.07 


9.27 


9.11 


9.23 


9.I0I 


9.19 


9.19 


13 


14 


10.07 


9.73 


10.03 


9.77 


9.99 


9.81 


9.94 


9.861 


9 90 


9.90 14 


15 


10.79 


10.42 


10.74 


10.47 


10.70 


10.51 


10.65 


10.561 


10.61 


10.61 15 


16 


11.51 


11.11 


11.46 


11.16 


11.41 


11.21 


11.36 


11.261 


11.31 


11.31 16 


17 


12.23 


11.81 


12.18 


11.86 


12.13 


11.92 


12.07 


11.971 


12.02 


12.02117 


18 


12.95 


12.50 


12.89 


12.56 


12.84 


12.62 


12.78 


12.671 


12.73 


12.73118 


19 


13.67 


13.20 


13.61 


13.26 


13.55 


13.32 


13.49 


13.38! 


13.43 


13.43119 


20 


14.39 


13.89 


14.33 


13.96 
14.65 


14.26 


14.02 


14.20 


14.08: 

14.78^ 


14.14 
14.85 


14.14120 
14.85I2I 


21 


15.11 


14., 59 


15.04 


14.98 


14.72!!14.91 


22 


15.83 


15.28 


15.76 


15.35 


15.69 


15.42 


15.62 


15.49 


15.56 


15.56(22 


23 


16.54 


15.98 


16.47 


16.05 


16.40 


16.12 


16.33 


16.19 


16.26 


16.2623 


24 


17.26 


16.67 


17.19 


16.75 


17.12 


16.82''17.04 


16.90 


16.97 


16.97 24 


25 


17.98 


17.37 


17.91 


17.44 


17.83 


17.52 17.75 


17.60 


17.68 


17.68 25 


26118.70 


18.06 


18.62 


18.141 


18.54 


18.22 


18.46 


18.30 


18.38 


18.3826 


27 


19.42 


18.76 


19.34 


18.841 


19.26 


18.92 


[19.17 


19.01 


19.09 


19.0927 


28 


20.14 


19.45 


20.06 


19.541 


19.97 


19.63 


19.89 


19.71 


19.80 


19.80i28 


29 


20.86 


20.15 


20.77 


20.24 


20.68 


20.33 20.60 


20.42 


20.51 


20.51i29 


30 
31 


21.68 
22.30 


20.84 


21.49 


20.93 


21.40 
22.11 


21.03 
21.73 


21.31 


21.12 


21.21 
21.92 


21.21J30 


21.53 


22.21 


21.63 


22.02 


21.82 


21.92 31 


32 


23.02 


22.23 


22.92 


22.33 


22.82 


22.43 


22.73 


22.53 


22.63 


22.63132 


33 


23.74 


22.92 


23.64 


23.03 


23.54 


23.13 


23.44 


23.23 


23.33 


23.33,33 


34 


24.46 


23.62 


24.35 


23.72 


24.25 


23.831 24. 15123.94 


24.04 


24.04 34 


35 


25.18 


24.31 


25.07 


24.42 


24.96 


24.53124.86 


24.64 


24.75124. 75'35 


36 


25.90 


25.01 


25.79 


25.12 


25.68 


25.23 


25.. 57 


25.34 


26.46 25.46136 


37 


26.62 


25.70 


26.50 


25.82 


26.39 


25.93 


26,28 


26.05 


26.16 26.16137 


38 


27.33 


26.40 


27.22 


26.52 


27.10 


26.63 


26.99 


26.75 


26.87 26.87138 


39 


28.05 


27.09 


27.94 


27.21 


27.82 


27.34 


27.70 


27.46 


27.58 27. 58|39 


40 
41 


28.77 
29.49 


27.79 
28.48 


28.65 


27.91 


28.53 


28.04!28.41 


28.16 
28.86 
29.57 


28.28 


,?8. 28140 


29.37 


28.61 


29.24 


28.74 29.12 


28.99 


28.9941 


42 


30.21 


29.18 


30.08 


29.31 


29.96 


29.44[29.83 


29.70 


29.70142 


43 


30.93 


29.87 


30.80 


30.00 


30.67 


30.14:30.54 


30.27 


30.41 


30.41 43 


44 


31.65 


30.56 


31.52 


30.70 


31.38 


30.84^31.25 


30.98 


31.11 


31.11 44 


45 


32.37 


31.26 


32.23 


31.40 


.32.10 


31.54 31.96 


31.68 


131.82:31.82:45 


46 


33.09 


31.95 


32.95 


32.10 


32.81 


32.24 32 67132.38 


[32.53 32.53 40 


47 


33.81 


32.65 


33.67 


32.80 


33.52 


32.94133 38 


33.09 


i33.23|33.23 4/ 


48 


34.53 


33.34 


34.38 


33.49 


34.24 


33.64 34 09 


33.79 


1.33.94 33. 94'4S 


49 


35.25 


34.04 


3.5.10 


34.19 


34.95 


34.34I34 30 


.34.50 


i34.65 34.65 49 


60'35.97 


34.73 


35.82 


34.89 


35.66 


35.05i35.51 


35.20 


136.36 35. 36 j50i 


1 


Dcp. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


j Dep. Lat. 


6 


46Deg. 


45| Deg. 


45i Deg. 


45i Deg. 


45] 


Deg. JQ 



TBAVERSE TABLB. 



161 




Plate '> 




i- '■"", 




"/■ '- 





\ 



A. .^ 



\ I 



%■ 'J. 






■J^/y J 



\ 







--- jcl 




\ 








/5: 






g 


. 






6-S 










: 




H^M=^ 


d 








■ '^ JV 








7 


^r^ u-.. 








\ " 




l> 




"-^^ 






\ a Ft 


M 










ion 



'obacco P. 



A A A I L 



hioar P. 



Jtirc Plant f^ 



Ploughed L. 



Gardens 



Orchards 



Piatt 



CoUonP. 



-- -^ .y -^ 



Vmo vanl 






^«; «- -ir- i 









DETAILS OF LEAVES 



Oak .'^- ^ ' jfy Fruit 



(lusi- 



'/'^'' -//>-* _'' 






Fresh Marsh 



Heath 



Oak AVoQfls 




Salt Marsh 




3Ieadoi\'s 



// 



mD^'DS Iss. 



Scarped road 



Stone Fence 



Tiirnpiltt" i-oad 



(V;::s,-v:^: 



LogLivii^i. 



V v^ X WoodeiJ Fe ncf A/V\ 



JM/Wr// J'„H- 
fhl//,il/ /i>r I'll' 
/1,1/Uri/ /rr Mv 



0/riyi /-llrfrn/ 
amni^r/;, J}//,'., 

JJo. /I,/,,,/,,,/ 
J-'fltm/iy 



'"'""":" 




J/r„ 


r 




Mi// 


ar/.i 




/>,. 


.w. 




A., 


S/,,m 




/',: 


.r.s-/i 


,., 


Hi: 


■rii-r 


v/ 


Jhsl 


1'///, 


' 


Tr/,/1 


„r„„l 


■,;■„/ /; 


Ti/.i 


.,/,/, 





a 



I) 

h 



O 



Hill 



■V 



'^j> * «,* "(■> ** f 




HiSiilDS Jas- 



_.s 



'L^ 



' 


' 














, S'»,,iffiii iiiiikfBi iriibSAi/.s, 










v\-\^,\\\. 




- — . 


v-s-X/'/v-v 













£lare_G.=- 




S:uia t-l.Mltl 



isli weirs 



\ 



(^ 



>aiid always covered i >^i&tn.lsoTnetirm.s 



Lai 



Dire ctiuii olthe Tiirrent 



Jiocks sometiiues L 



SaVtt'^'aii^e-mai Lfflock- 















z-' 




U'^Mij^ 



)v^ 



Mil ] I 0>N 



■"^^ 



Teaiii1>oat fecrv 



Vb 



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LIBRARY OF CONGRESS 

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020 365 744 4 




